You have to add „location=paragraph” to the textbackground setup.
\definetextbackground
[ChapterFrame]
[frame=off,
background=color,
backgroundcolor=green,
backgroundoffset=1ex,
location=paragraph] % default: location=text
\definehead [Framed] [chapter]
\definehead [Frameless] [chapter]
\setuphead
[Frameless]
[before={\blank[2*line]}]
\setuphead
[Framed]
[page=no,
before=,
beforesection={\page\blank[2*line]\starttextbackground[ChapterFrame]},
aftersection=\stoptextbackground]
\starttext
\startnamedsection[Frameless][title=Chapter without frame]
\input knuth
\stopnamedsection
\startnamedsection[Framed][title=Chapter with frame]
\input knuth
\stopnamedsection
\stoptext