As already stressed in https://tex.stackexchange.com/a/137031, this answer should be considered a workaround: the correct solution would be to "wait for the feature request in tikz".
Naturally, that can take longer than having a clumsy work-around at hand.
Here is an attempt to use a pgfplots surface plot to simulate your desired filled shading:

\documentclass[a4paper]{article}
\usepackage[cmyk]{xcolor}
\usepackage{pgfplots}
\pgfplotsset{compat=1.9}
% if you have v1.8, write:
%\pgfplotsset{mesh/colorspace explicit color output=cmyk}
\begin{document}
\begin{tikzpicture}
\draw (0,0) grid (3,3);
\shadedraw
[shading=axis,left color=green,right color=orange,color=blue,line width=2]
(2,0) -- (2,1)
{[rounded corners=1em] -- (3,1)} --
(3,0) -- (2,0);
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,0) grid (3,3);
\draw
[color=blue,line width=4pt]
(2,0) -- (2,1)
{[rounded corners=1em] -- (3,1)} --
(3,0) -- cycle;
\clip
(2,0) -- (2,1)
{[rounded corners=1em] -- (3,1)} --
(3,0) -- cycle;
\begin{axis}[
% necessary to match up coordinate systems:
xmin=0,ymin=0,
anchor=origin,
x=1cm,y=1cm,
hide axis,
]
\addplot[surf,mesh/color input=explicit,shader=interp]
table[meta=cdata] {
x y cdata
2 0 color=green
2 1 color=green
3 0 color=orange
3 1 color=orange
};
\end{axis}
\end{tikzpicture}
\end{document}
Both are tikzpictures, the first one is replicated from your question and the second one is based on pgfplots. You see that it is considerably more involved: it installs a clip path to restrict the shading to your "rounded" rectangle, then it draws the outline of the clip path (for some reason, pgf rejects it if I say \draw[clip] with the remaining options). The rest is a pgfplots axis which is forced to use the same coordinate system as the outer tikz picture (requiring a bunch of keys explained in section "TikZ interoperability" in the pgfplots manual).
This answer will hopefully become superfluos once TikZ supports CMYK shadings.