Hey man, that's some creative thinking right there. I see what you're trying to do.
To answer your question, no, the engine vacuum won't open the choke for you. The choke plate is usually too heavy and isn't designed to be moved by air like that.
I've been down that road before, trying to make a wrong part fit on my old tiller. I think your idea of rigging a simple manual cable to the handle is probably your best bet if you want to make that carb work.
Honestly, sometimes it's just easier to get the right part in the first place and save the headache.
Good luck with the project, hope you get it running.