Yes, you can use additional styles with the DGX-650, but to my knowledge you can't add new voices to it as you can with the higher-end PSR-S and Tyros models.
Something else you might want to know is that the DGX models-- along with the PSR-E models-- can play only two Main style variations (A and B), so if you get a style file that contains four Main style variations (A, B, C, and D) you won't be able to select all of them. However, there are several utility programs for working with Yamaha styles, and you can easily take a 4-variation style file and create new 2-variation style files from it, selecting which two parts of the original file you want to include in the new files.
Another thing you need to know about style files is that they're often tailored for specific keyboards, by which I mean the voices they use and other things like DSP effects are available on a particular model but might not be available on other models. For this reason you may also need to use one of those style utilities to change the voices in a style file so they're ones that are available on whichever model you happen to have.
