The Gauntlet and PuPuPeril adventure paths are mutually exclusive- you can only do one. The intent (wibbly-wobbly timey-spacey compression permitting) is that while some of the Gauntlet is going on and everyone's paying attention to that, the PuPuPeril group skitters off into the rest of PuPuLand to try and "acquire" a smol blue friend or twenty.

However, as it's a highly televised event, it'd be possible for PuPuPerileers to try and watch the live feeds of the event and keep track of what's going on and heckle their friends later, at least until everything goes to PuPu.