I met both of my agents at conventions, though I was not pitching work at the time.
I met the first agent at a World Fantasy Convention, where he heard me read some of my work, and asked if I had longer mss available. (Long story short, I did, he tried, no go, we parted ways amicably eight years later.)
The second agent and I crossed paths at a local RWA event. I was impressed with her knowledge, enthusiasm, and grit; I also knew that she wasn't taking on new clients unless she'd met them & had a rec from one of her current authors. A year later, when I had a sticky situation with the contract for my debut novel, I politely asked (okay, I begged) a couple of her clients to put in a word for me. She and I chatted, I amused her or something, so she took on that contract and made it safe for me. She's been incredible ever since.
Like the OP, I don't have a lot of money for conventions. So if and when I go, I try to gain as much from the total experience as I can. (Ben has great advice on this!) If I was back to pitching agents again, I probably *wouldn't* do it at a con, or not seriously. Everyone else is, for one thing. I'm terrible at speed pitches. And I want my query and sample pages to do most of the work for me.