Yep, but only the bus-sized ones from the Saratoga at the beginning of DS9.
In terms of the size of the required technology, there SHOULD be no reason they wouldn't have some form of warp drive aboard, but Trek in general says that FTP travel requires antimatter-level power; this generally means that they don't want to have dozens of small craft with tiny warp cores aboard to constantly maintain.
OTOH, we've seen them stuff a warp drive AND a person into a probe casing for some rather uncomfortable transportation in urgent circumstances, so it DOES happen.
Mark
Not necessarily. A small fusion core would probably also allow for warp propulsion. It wouldn't be very fast, but it would probably still be better than sublight, and allow to go to a nearby system, and wait for help.
...Depends on how good shuttles are at towing things at warp. This whole "extending a warp field" business might be the privilege of larger vessels in general.
The Constellations certainly seem to have a large number of shuttlebays in the saucer.
A number of bays of some sort, at any rate. For all we know, the bow shutters cover a navigational deflector, and the side shutters hide sensors or cargo holds. Plus at least one facility for the quoted shuttlecraft, of course.
Timo Saloniemi
It could easily be the responsibility of any surviving shuttlecraft to tractor the pods to the nearest planet-habitable if possible, one at a time, if necessary (or at least as long as the fuel holds out).
I imagine that a standard shuttlecraft could carry at least one pod, while the bigger ones might be able to carry two or three at a time.
Any runabouts onboard, if they survived of course, could probably carry even more at warp, and hopefully make enough trips, assuming their fuel reserves were topped off at the time. Even then, if there is a nearby nebula, well, those bussard collectors are there for a reason.
And the captain's yacht would also be useful for that as well, and if she still has enough fuel after getting the lifepods to some sort of safety, might even go off to get help, or scout for a more habitable planet.
At least that is how I imagine the directive for the evacuation of a starship would be like, assuming there is enough time to get all of the shuttles, runabouts, and the yacht clear.