I'm not a climber, but I was wondering:

Could you friction knots to make paracord descenders that could control your speed? E.g., like one of the knots here: http://www.chockstone.org/TechTips/Prusik.htm?

Or, assuming you have enough paracord, quadruple it up and twist to make a larger bundle, then do a leg wrap or dulfersitz for a controlled descent. Specifically, I'm thinking about the "Surviving Disaster" Towering Inferno episode (see Part 6).

Ultimately, if you are planning for a situation of this sort, then better to prepare adequately than rely on something that is not suitable for the task. It seems to me that you can get a starter kit with 100' rope, bag, figure-8 and carabiner for around $150, and spend another $30-50 on a harness. There are also emergency building escape kits, primarily designed for firefighters, running between $150 and $200 (plus harness).

With lift tickets running over $60/day, if this is a potential risk for you, the $200 seems a reasonable precaution. Many skiers spend more than that just on their boots.

Finally, you there was a lengthy discussion about using paracord to repell out of buildings in this thread:
http://forums.equipped.org/ubbthreads.php?ubb=showflat&Number=187229&page=1