We asked for no presents for ds1 when he turned 2, as his birthday is in early January and we had his naming ceremony just before Christmas. He had a joint naming ceremony/birthday party type bash, and we asked people to make a donation to charity in his name, as with Christmas and birthday coming up, we felt he'd be a bit overwhelmed. It was actually really nice to see what people did with their donations, they did some lovely things in his name then gave us the cards and info about what they'd done, which are in his memory box. People still gave him presents, but we weren't upset by that, it was their choice, we just weren't overwhelmed with tons of crap that we had no room for :-) It might be wise to suggest that you don't want people to feel they have to buy him a gift, as opposed to a flat out 'no presents' as some people do like to re-gift after Christmas (the joys of a January birthday, my eldest has had some stink re-gifted gifts over the years!) and some people love buying gifts for children, so you can't really dictate that they absolutely can't.
Mind you, I'm the arsehole mum who once gave out a wrapped muffin with a card saying we'd donated to a local charity instead of doing party bags at his 4th birthday party too, and I'm not sorry, and don't feel mean.
With 3 dc, we used to feel like we had tat overload sometimes, so if you can manage it, then why not?! As they've got older they prefer money/vouchers anyway, to put something bigger than they're saving for, and it's normal for our older children's friends to get a £10/£5 in a card and a box of Maltesers/sweets. So much easier and less stressful.