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Google will see, to all intents and purposes, a new page - same name, new content, just as if you'd manually updated it.
However, what Google will NOT see is a fresh page-modified date when it interrogates the file. For that reason, I suspect Google may well not be that interested in fetching the file.
On one of my sites, I have a static page that has a META refresh to a page that changes almost daily. Google looks at the static page and seldom retrieves it to see what's in there - last time was August 27th.
DerekH
If it's on a UNIX system, the solution to your problem is as simple as putting "touch *.html" in a crontab file. "man touch" and "man crontab" at the command line to find out what I'm talking about.
Caveat: Some Apache server configurations don't put Last-Modified dates on SSI-ed files unless you use the "XBitHack" directive.