In the case of the domain root itself - Google should have it indexed as just the domain root, and not index.html. If that is the case, then changing just that one page to php should not cause you any trouble. However, if Google has your page indexed with both urls, your rankings may already be tangled up just a bit.
However, you can set a server to parse php script within the page's source code - even though the extension remains .html. That's an issue that has come up a couple thousand times in our PHP forum [google.com], and taking that approach would make your whole concern evaporate.