If they show as points in your HHonors account, they do count as "activity". The thing to watch out for with Hilton is their shorter-than-usual expiration, of just 12 months. Hilton has two no-annual-fee-ever credit cards, one from Citi and one from Amex. If it's not always easy for you to dine or stay with them at least once a year every year, you may want to get one of those cards. It'll give you tens of thousands of points as a signup bonus (if you do a modest amount of spend over the first few months), but beyond that, if you use the card for something at least once a year (or to be safer two times a year), you'll have activity in HHonors keeping your HHonors account alive and you'll have activity on your card keeping the bank from cancelling the card for inactivity. (Yes, banks do that too!)

Here's the FT thread for the Citi card (which I think has the bigger signup bonus right now):