Yes, if I understand what you want to do then registrations should help.
Note, I do not have any experience with the DGX models, but the PSR-E models that I own have very similar capabilities as far as their registrations-- 8 banks of registrations, each containing 4 registrations.
Before saving any registrations, you'll probably want to think about how you want to organize them, because you'll want to be able to switch between registrations while playing using a single button whenever possible, since switching between registration banks requires additional button presses. Consequently, you don't want to have to switch to a different registration bank when timing is critical; it's better to switch the registration bank when you have a bit more time, such as between songs, or if you're able to take a short pause in your playing while the style continues to play.
To switch to a particular registration bank, push the BANK button, then use the numeric keypad or dial to select the desired registration bank number.
Once you've switched to the desired registration bank, you can save 4 registrations to it. To save a registration, hold down the BANK button (to activate its secondary function as the REGIST MEMORY button) and push the button for the desired registration, 1 through 4. The keyboard's current settings will be saved to the selected registration.
To recall a registration, all you need to do is push the appropriate registration button-- as long as you're already in the appropriate registration bank, otherwise you'll need to switch registration banks first.
Just about the only thing you need to worry about is that switching registrations will normally switch to the style-related settings that were saved in that registration, which might not be what you want to have happen. However, if you push the SONG button before you save a registration, the keyboard won't save the style-related settings to the registration. Then you'll be able to recall that registration without it changing whatevee style happens to be playing.