Is it possible to detect to see if a browser has support for hardware accelerated page rendering and is it also possible to see if it has been enabled? I am aware that Firefox 4, IE9 and Chrome support it, but it may or may not be enabled due to the version of the browser, the OS, and the computer hardware itself.
Is this possible using some form of DOM sniffing?
Like all other browser-specific capabilities, probably the best thing you can do is to devise some sort of feature test and actually measure the performance of what matters to you.
You can do when the first page on your site is loaded and then set a cookie with the setting so you only have to do it every once-in-a-while and don't have to do it again for awhile as long as the cookie is present.
Depending upon what type of performance you care the most about, you can devise a test that's pretty specific to that. For example if you cared a lot about image scaling, you could devise a JS test that scales an image among a bunch of different sizes in a big enough loop to get a measurable time and then decide what your timing threshold is.
Not only would this be better than a single binary choice of accelaration on or off, but it would also be able to test the specific features you care about and be able to see how fast they actually are.