Google Forms appends each form submission as a rows in a spreadsheet, and isn't limited that way.

Of course, some account has to own the spreadsheet and hence have write access. So it's not the ideal vote-tallying system.

Although all edits are logged...

Wouldn't this whole system be fine with a Google Form submitted to a Doc?

I wonder if you could get around that by giving groups of caucus precincts a five minute time slot?