That's a great question, and the answer unfortunately is no.
Reason being, is that it only streams MIDI and not audio through USB, however the Rec 'N' Share App will be compatible with most DTX kits in the future, not just yet though. It's currently just available for the 402 series and the EAD10.
If you want to record your 502 performance, I might recommended taking two L/R quarter inch Mono's from the module into an interface, then connect a USB A/B cable from the interface into your laptop where your DAW is held.
If you don't want to go into an interface, you could just send MIDI info from the module directly into your laptop, again using a USB connector.
From that point, even something as basic as iMovie, or Adobe Premiere can be used to pull your audio and video together, and with a little editing, you can have a recording that way.
I hope that helps Eliran, and sorry for the bad news!