Oh yeah.. that's right.
so I just had another look, and I really think the short answer is "no".
The long answer:
You can extend simple search
to look at custom tables I've never used simple search, but I don't think that searching the modx_site_tmplvar_contentvalues table will help, because I assume that you're template variables actually contain a reference to a chunk? (I'm guessing) rather than the content itself.
Sure you could maybe hack something together using simpleSearch and some custom snippets, but I think it would be a lot of work for a result which is absurdly inefficient.
I might be able to think of a workaround, but I need more.. is the raw sidebar content actually in the template variable? or do you put a chunk call in the template variable? are you ok with making a custom snippet (not necessarily guru status.. just a few lines of php) or does it have to use existing chunks and plugins?