My best friend recently got engaged and it was all very awkward for me because she was actually in the process of dumping him (I was supporting her in this) when he proposed, and she said yes.
I had to go from 'oh my god yes, he's so not right, yes, you are doing the right thing, it hurts just now but you'll move on etc etc' to going 'oh right! er, great! hurrah!' - it was a total cringe.
I didn't send a card or anything - I felt so confused and odd about it. But everybody else rained down cards, champagne, and presents on them until I felt really awful about it all and wished I'd just given them a card at the beginning.
Anyway, they then had a party 'to let our friends meet each other' which turned out to be an engagement party in (thin) disguise, again with presents, champagne and flowers galore. Again, I turn up with beer and crisps and feel like I have hideously misjudged yet again. Aargh!
Anyway, roll on the wedding. Even I know how to behave and what to bring to one of those!
(sorry, the point of all this was to say that yes, people do very much give engagement presents, even to edgy urban types who would have laughed at the concept until they got the 'diamond fever')