If the jackpot is big enough pretty sure there is value in all pocket pairs, and eventually all suited connectors, even with gaps. See the flop even for a raise or two, but tighten up if you don't hit a jackpot draw.
If you have a big hand or big draw it is often better to bet small or call so everyone can get to the river. This is especially true if you think your opponent has a big hand.
If you're talking about BBJ where quads have to be beaten, then you make virtually no adjustments to your play. You might slowplay a flopped quads for one street since the value of letting someone catch up is very slightly higher in a BBJ game. Otherwise, don't delude yourself into thinking the BBJ justifies calling a raise preflop out of position with your garbage 35s.
For other promotions, you have to understand the requirements and determine if they require play adjustments. For example, if you are going to get $5,000 for a royal flush and flop 4 to the royal, then you probably need to check call to the river as your EV from the promo is > $100 and is most likely greater than the EV you give up by not betting.