When we got married, we were 39 and 41 and already had a house full of two people's stuff (albeit nothing fancy), so we said "no gifts" on the invitations. Also, it was a really basic wedding at the courthouse, followed by a late lunch at a restaurant for the 20 people who came. A few days later, we had a party at our house and invited everyone we knew, cooked most of the food ourselves. We called it an "open house" because there was no way all those people would fit at one time, though it did get crowded (it was fun).
Even with all that, we still got a few presents, including cash gifts from relatives. We sent thank-you notes to all of those people.
It's 20 years later and we're still married, so I guess everything worked out.
I think as long as you're polite, it's okay to do whatever you want, certainly with regard to gifts/no gifts.