You should be fine as long as you don't twist around during your maneuvers and the release tension isn't too low. Actually, have a gander at Look and Speedplay clipless systems. It'll probably work out better on a fixed drive-train than eggbeaters. I haven't tried out eggbeaters myself, but from what I've read, they release pretty easily. Look and Speedplay (others, too) are very secure.
If you want extra security, you can fit some clipless pedals with toe straps. Some have release levers, too. I'd say it's overkill unless you're racing.
Hey Billy. Yeah, ignore my advise about the Look and Speedplay options. Go with Michael's about ATAC, eggbeaters, SPD. You'll dig that better. You've probably seen all the nice sneaker-y options that'll accept two bolt recessed cleats. Give that a try. It's good stuff.
I run Look pedals on one bike and SPDs on another. Very happy with how it works out - each has it's own purpose. Recessed cleats are way more convenient for gettin' around and sloppy weather.
i run eggbeaters (and kursk pros) on one of my fixed gears, and clips and straps on my other one. the eggbeaters are a ton better, and arent even bad when it comes to panic-escaping quickly. i also ran shimano SPD pedals for a bit before that, and those weren't nearly as nice to get in and out of as the eggbeaters. and they've always been nice to me while skidding.
clipless pedals on a fixed gear are definitely a good move as an alternative to the straps and such.
I echo the good reviews for the eggbeaters/candy pedals. Easy to get out of in an emergency, walkable/minimal cleats, but you can do a full sprint and not worry about accidental exit. IMO the best option for all of commuting/casual riding/racing (cross, mtb.).