If a customer earns a gift card, do they also get their loyalty stamps on that order?

Yes. The two do not get in each other's way. Stamps accrue on the order the way your loyalty programme says, and the earned card rule is checked separately when the order completes. One of the five rules, Loyalty cards completed, even builds on stamps: it hands out a gift card when a customer has filled a whole stamp card a set number of times. The other four count orders, days ordered on, total spent and years since the first order, and work with no loyalty programme at all. Both are set up under Marketing: Loyalty & stamps for the stamps, Gift cards for the rules.