Edit: What if the background is not white? asked by egreg
So I mimic a scenario with a background to verify the logic.
Code
\documentclass[border=0.3cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{chains,backgrounds}
\begin{document}
\begin{tikzpicture}[%
start chain=going below,
every node/.style={%
join,
on grid,
on chain,
draw,
align=center,
},
every join/.style={->,draw}
]
\tikzset{
none/.style={->,cyan,line width=5pt}, % remove line width see the artifact
}
\node (a0) {A0};
\node {B0};
\begin{scope}[every join/.style={->, shorten <=5pt,shorten >=5pt}]
\node [join=by none,right=of a0] (a1) {A1};
\begin{pgfonlayer}{background}
\draw[fill=cyan] (-0.5,-1.5) rectangle (1.5,0.5);
\end{pgfonlayer}
\end{scope}
\node {B1};
\end{tikzpicture}
\end{document}
Here is a possible solution to reverse the default mentioned in the comment by the OP. The logic behind the solution is to use a scope environment to reverse the default by drawing a shorter connection line, then draw a thick line with white color to erase the short line. The erase action is defined by the none macro.
\begin{scope}[every join/.style={->, shorten <=5pt,shorten >=5pt}]
<node commands>
\end{scope}
none/.style={->,white,line width=5pt}, % remove line width see the artifact

Code
\documentclass[border=0.3cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{chains}
\begin{document}
\begin{tikzpicture}[%
start chain=going below,
every node/.style={%
join,
on grid,
on chain,
draw,
align=center,
},
every join/.style={->,draw}
]
\tikzset{
none/.style={->,white,line width=5pt}, % remove line width see the artifact
}
\node (a0) {A0};
\node {B0};
\begin{scope}[every join/.style={->, shorten <=5pt,shorten >=5pt}]
\node [join=by none,right=of a0] (a1) {A1};
\end{scope}
\node {B1};
\end{tikzpicture}
\end{document}
\makeatletter\tikzset{no join/.code={\let\tikz@after@path=\pgfutil@empty}}might give a useableno joinkey. – Mark Wibrow Jan 17 '15 at 12:36