Definitely. Can some of them fit into a small, woman’s clutch?
Probably not, but you can fit a decent quality tent in a small hatchback.
I think it’d be smart to keep stuff in your car, just in case. If you can spare the room.
With a little planning and piecemeal work, you can get quite a kit together that would put you ahead 90% of the general population. Even enough to get you through a week of Storm Sandy or Katrina or whatever else could happen could mean all the difference in the world.