Yes, it's possible, and you have several options depending on the desired result. Below I show six different possibilities.

The code:
\documentclass{article}
\usepackage[vmargin=1cm]{geometry}
\usepackage{amsmath}
\usepackage[many]{tcolorbox}
\usepackage{empheq}
\begin{document}
\begin{empheq}[box=\fbox]{gather}
Eq1
\\ Eq2
\\ Eq3
\\ \notag\text{where variables ... are defined as}
\\ Eq4
\\ Eq5
\end{empheq}
\begin{empheq}[box=\fbox]{gather}
Eq1
\\ Eq2
\\ Eq3
\\ \notag\text{\parbox{.7\linewidth}{where variables ... are defined as}}
\\ Eq4
\\ Eq5
\end{empheq}
\begin{empheq}[box=\tcbhighmath]{gather}
Eq1
\\ Eq2
\\ Eq3
\\ \notag\text{where variables ... are defined as}
\\ Eq4
\\ Eq5
\end{empheq}
\begin{empheq}[box=\tcbhighmath]{gather}
Eq1
\\ Eq2
\\ Eq3
\\ \notag\text{\parbox{.7\linewidth}{where variables ... are defined as}}
\\ Eq4
\\ Eq5
\end{empheq}
\begin{tcolorbox}[enhanced,oversize,breakable,colframe=cyan,colback=cyan!20,top=-\abovedisplayskip,bottom=0pt]
\begin{gather}
Eq1
\\ Eq2
\\ Eq3
\end{gather}
where variables ... are defined as
\begin{gather}
Eq4
\\ Eq5
\end{gather}
\end{tcolorbox}
\noindent\makebox[\linewidth]{\fcolorbox{orange}{orange!10}{%
\begin{minipage}[t]{\linewidth}
\vskip-\abovedisplayskip
\begin{gather}
Eq1
\\ Eq2
\\ Eq3
\end{gather}
where variables ... are defined as
\begin{gather}
Eq4
\\ Eq5
\end{gather}
\end{minipage}}}
\end{document}
Explanation
In options one through four, instead of two gather environments I used just one. The text was written using \text.
In options two and four, the text was additionally placed inside a \parbox, so you can control its width and have possible line breaks.
Options one and two use a standard empheq environment with \fbox as the framing method.
Options three and four use the interaction between tcolorbox and empheq; the framing method is \tcbhighmath.
In option five, a tcolorbox was used to surround both gather environments and the text; page breaks are allowed.
In option six, a \fcolorbox was used to surround both gather environments and the text; page breaks are not allowed since a minipage was used.
boxruleas in\begin{tcolorbox}[oversize,breakable,colframe=cyan,colback=cyan!20,boxrule=0.4pt] ...\end{tcolorbox}(change0.4ptto the desired value.) – Gonzalo Medina Jul 25 '15 at 17:47I'm getting an error
" Illegal unit of measure (pt inserted).
ptpart (probably a result of copy-paste). Delete0.4 ptand write it again directly from your keyboard. – Gonzalo Medina Jul 25 '15 at 18:04breakablefrom thetcolorboxoptions and no page breaks will occur. – Gonzalo Medina Jul 25 '15 at 18:31enhancedto the options:\begin{tcolorbox}[enhanced,oversize,breakable...]. I've added this as an edit. – Gonzalo Medina Jul 26 '15 at 19:03enhancedbyenhanced jigsaw. – Thomas F. Sturm Jul 27 '15 at 05:35