Yes, mixing and recording are separate things and not influencing each other. The only thing you have to decide for recording is if the "Digital Send Options" for each channel shall be pre or post Fat Channel processing. When you load the template for your mixer in Studio One, all routing is already set. Channel 1 is recorded on track 1, 2 on 2 and so on.
The 24R has no DAW mode, therefore you can't make any aux or cue mixes in Studio One. You can (and should) run UC Surface parallel to Studio One on your computer.