The answer was brief and simple, "No."
An engagement party isn't about gifts. It's about an announcement of a couple's commitment to close friends and family. Usually if you make the engagement party cut, you'll be invited to the wedding and probably a bridal shower. You'll have ample opportunity to spend money, don't forget the outfit you'll wear to the wedding and travel expenses if it's going to be a destination wedding.
Some people feel compelled to take presents even if there is a request for no presents on the invitation. This could pose discomfort to those who adhered to the request. There is nothing worse than sharing an elevator with people going to the same party with some holding presents and others not. If you're holding a present, be discreet when you give it. No need to announce, "This is for youuuu." Then the poor receiver has to say, "Oh, you didn't have to do this." This gets dull quickly.
Some people just can't help themselves. They just have to give presents. That's fine but not at the party. You can send a gift or give one in person on another occasion like dinner or over a drink - you should probably pick up the tab too.
We've talked about gifting before. It seems to become a problem when the giver thinks it's all about them and has little to do with the person who will be receiving the present. Some use it has an opportunity to posture in front of others. "I'll show them who has manners!"
Well show them. If you're asked not to bring a present don't.