There may be the odd exception, but on the whole... no. Sorry.
Mainly for the reason you mention - do something weird on your rig and the live sound guys have no signal. And if you need to trim your input gain, their mix goes up the swanee.
Also, it means you would be feeding them line level, and if you're patching into the stagebox, most of those lines will be directly hooked up to their mic inputs.
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Basically, if you present this idea to most live sound people, you'll get raised eyebrows and probably a complete lack of cooperation. Venue techs are not fans of anything that is likely to jeopardise getting their side of the job done.
If you're stuck for budget you may just have to go down the direct outs route. But the feasibility of this will, as you say, depend on the venue. It could work out if you restrict your operation to a few venues who you've struck up a good relation with.