It is not completely clear to me what you are trying to achieve and why do you want to overlap lines, so I’ll stick to the question “Is there a command that can add vertical space before a line of text?”.
The pdfTeX engine has a \vadjust pre primitive that can conveniently be used for this. See the following MWE.
% 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
\newcommand*\vspacebeforeline[1]{%
\ifvmode % if in vertical mode, act as "\vspace{#1}"
\vskip #1
\vskip \z@skip
\else
\@bsphack
\vadjust pre {%
\@restorepar
\vskip #1
\vskip \z@skip
}%
\@esphack
\fi
}
\makeatother
\begin{document}
Here is some nonsensical text, written for the sole purpose of filling up at
least one line. Well, after all I~think that two lines would be even better.
And now, we use our new command exactly here\vspacebeforeline{18pt plus 6pt
minus 6pt}, followed by a few other words to end the test.
\vspacebeforeline{3pt}
It can be used in vertical mode, too.
\end{document}
This is the output it produces:

\main {This text is written using command main}\mainv {This text is written using command mainv}– Matt Jul 12 '16 at 15:18\maindefined? – Mico Jul 12 '16 at 18:32\documentclassare you using? It could be that the document class defines\parskipto be non-zero, and that's the space that you're seeing. – Werner Jul 12 '16 at 19:01\hspace*{0pt}\ignorespacespart of the macro(s)? – Mico Jul 12 '16 at 19:07