I do both, mostly the latter as I am usually wanting the cloves to stay in the stock. If I don't, I do the former.
One thing you can do, if you like the idea for your buddy's thing: roast a lot of garlic heads ahead of time, one each per serving of the boil, making sure that they are not over-carmelized which can make the garlic bitter (to avoid this I roast, enclosed in foil, at 350 - not the higher temps one often sees called for). Cool completely, cover, fridge to hold. When needed either rewarm or simply bring to room temp. Place a roasted garlic head in each serving bowl, top with a pat of butter and then hot broth, shrimp, potatoes, corn, etc., and serve with plenty of crusty bread for dipping (and to smear with the roasted garlic).