The order in which you combine the two skips (the \leaders and the non-\leaders one) doesn’t matter: they will always vanish as a unit.
% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly
% declare the paper format.
\usepackage[T1]{fontenc} % Not always necessary, but recommended.
% End of standard header. What follows pertains to the problem at hand.
\makeatletter
\newsavebox@NWD@dot@box
\newlength@NWD@space@skip
\newcommand*\numberwithdots[1]{%
\unskip
\setbox@NWD@dot@box \hbox{.}% use current font
@NWD@space@skip
\fontdimen\tw@ \font
@plus \fontdimen\thr@@ \font
@minus \fontdimen 4 \font
\hskip \glueexpr @NWD@space@skip-\wd@NWD@dot@box
\cleaders \copy@NWD@dot@box \hskip \wd@NWD@dot@box
#1%
\cleaders \copy@NWD@dot@box \hskip \wd@NWD@dot@box
\hskip \glueexpr @NWD@space@skip-\wd@NWD@dot@box
\ignorespaces
}
\makeatother
\begin{document}
\numberwithdots{1} note that the indent does \emph{not} count as a ``begin of
line'': not sure if this is what is wanted. Some text \numberwithdots{2} that
includes \numberwithdots{3} some numbers: I~hope that \numberwithdots{4} some
\numberwithdots{5} of them will fall \numberwithdots{6} on a line boundary,
although \numberwithdots{7} it is \numberwithdots{8} always possible
\numberwithdots{9} to arrange things in order \numberwithdots{10} to make
\numberwithdots{11} this happen. And it \numberwithdots{12} is also
possible\linebreak[4] \numberwithdots{13} to force \numberwithdots{14} a line
\numberwithdots{15} break\linebreak[4] at a specific \numberwithdots{16}
position.
Two numbers in a row, though, do not \numberwithdots{123} \numberwithdots{456}
look well.
\end{document}
This is the output I get:

Addition
Perhaps, it would be preferable to use wider spaces around numbers with dots; and it would be even better to allow the user to customize this aspect.
% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly
% declare the paper format.
\usepackage[T1]{fontenc} % Not always necessary, but recommended.
% End of standard header. What follows pertains to the problem at hand.
\makeatletter
\newsavebox@NWD@dot@box
\newlength@NWD@space@skip
\newcommand@NWD@factor{1.5} % redefine default as you please
\newcommand\numberwithdots[1]{%
\unskip
\setbox@NWD@dot@box \hbox{.}% use current font
@NWD@space@skip
@NWD@factor\fontdimen\tw@ \font
@plus \fontdimen\thr@@ \font
@minus \fontdimen 4 \font
\hskip \glueexpr @NWD@space@skip-\wd@NWD@dot@box
\cleaders \copy@NWD@dot@box \hskip \wd@NWD@dot@box
#1%
\cleaders \copy@NWD@dot@box \hskip \wd@NWD@dot@box
\hskip \glueexpr @NWD@space@skip-\wd@NWD@dot@box
\ignorespaces
}
\newcommand\nwdsetdotspacing[1]{\def@NWD@factor{#1}}
\newcommand\nwdlinebreak{\unskip\unskip\linebreak}
\makeatother
\begin{document}
\numberwithdots{1} note that the indent does \emph{not} count as a ``begin of
line'': not sure if this is what is wanted. Some text \numberwithdots{2} that
includes \numberwithdots{3} some numbers: I~hope that \numberwithdots{4} some
\numberwithdots{5} of them will fall \numberwithdots{6} on a line boundary,
although \numberwithdots{7} it is \numberwithdots{8} always possible
\numberwithdots{9} to arrange things in order \numberwithdots{10} to make
\numberwithdots{11} this happen. And it \numberwithdots{12} is also
possible\nwdlinebreak[4] \numberwithdots{13} to force \numberwithdots{14} a line
break \numberwithdots{15}\nwdlinebreak[4] at a specific \numberwithdots{16}
position.
Two numbers in a row, though, do not \numberwithdots{123} \numberwithdots{456}
look well.
\nwdsetdotspacing{} % empty argument amounts to 1
\numberwithdots{1} note that the indent does \emph{not} count as a ``begin of
line'': not sure if this is what is wanted. Some text \numberwithdots{2} that
includes \numberwithdots{3} some numbers: I~hope that \numberwithdots{4} some
\numberwithdots{5} of them will fall \numberwithdots{6} on a line boundary,
although \numberwithdots{7} it is \numberwithdots{8} always possible
\numberwithdots{9} to arrange things in order \numberwithdots{10} to make
\numberwithdots{11} this happen. And it \numberwithdots{12} is also
possible\nwdlinebreak[4] \numberwithdots{13} to force \numberwithdots{14} a line
break \numberwithdots{15}\nwdlinebreak[4] at a specific \numberwithdots{16}
position.
\nwdsetdotspacing{2}
\numberwithdots{1} note that the indent does \emph{not} count as a ``begin of
line'': not sure if this is what is wanted. Some text \numberwithdots{2} that
includes \numberwithdots{3} some numbers: I~hope that \numberwithdots{4} some
\numberwithdots{5} of them will fall \numberwithdots{6} on a line boundary,
although \numberwithdots{7} it is \numberwithdots{8} always possible
\numberwithdots{9} to arrange things in order \numberwithdots{10} to make
\numberwithdots{11} this happen. And it \numberwithdots{12} is also
possible\nwdlinebreak[4] \numberwithdots{13} to force \numberwithdots{14} a line
break \numberwithdots{15}\nwdlinebreak[4] at a specific \numberwithdots{16}
position.
\end{document}
Unfortunately, for a TeXnical reason, in order to force a line break, we also had to replace the \linebreak command with our \nwdlinebreak.
Output:

An additional degree of freedom: a factor also for the amount of backspacing. In addition to this, the following code excerpt presents an alternative, and more robust, implementation:
\makeatletter
% Alternative approach that permits nesting: use temporaries, but with grouping:
\newcommand@NWD@dot@factor{}
\newcommand@NWD@spc@factor{1.5}
\newcommand\numberwithdots[1]{%
\unskip
\setbox\z@ \hbox{.}% use current font
\dimen@ @NWD@dot@factor\wd\z@
\skip@
@NWD@spc@factor\fontdimen\tw@ \font
@plus \fontdimen\thr@@ \font
@minus \fontdimen 4 \font
% More elegant with subroutines (or perhaps not):
@NWD@nonleader@hskip @NWD@leader@hskip
{#1}%
@NWD@leader@hskip @NWD@nonleader@hskip
\ignorespaces
}
\newcommand@NWD@nonleader@hskip{%
\hskip \glueexpr \skip@-\dimen@ \relax % for robustness
}
\newcommand@NWD@leader@hskip{%
\cleaders \copy\z@ \hskip \wd\z@
}
\newcommand\nwdsetdotspacing[2][]{%
\def@NWD@dot@factor{#1}%
\def@NWD@spc@factor{#2}%
}
\newcommand*\nwdlinebreak{\unskip\unskip\linebreak}
\makeatother
Further readings
The trick of including a box in a glob of glue as \leaders, in order to have it disappear at line or page breaks, is well known: as far as I can tell, it was first proposed by Marcin Woliński in 2007, see How to make a box disappear at a line break.
See also: