After learning I had a slow PS fluid leak in the rack and pinion that I couldn't afford (~$800), I was going through about 1 bottle every 24 hours. The other day, I was driving, heard a noise and had smoke coming from the hood and power steering went completely out. I'm guessing something like a hose or something went. My question is if my car is ok to drive with no power steering fluid running through the system at all. I would only be driving for a period of around 10 minutes or so - no long durations. Could I possibly burn something else up and royally screw up the car? Any insite would be helpful.

With no fluid in the PS system, at a minimum you will mess up the PS pump. Then you will also have to deal with the danger of not having control of the steering system due to lack of "assist" from the hydraulics (on non-thereof) and the fact that steering will be "loose" but "heavy" due to the lack of fluid. The universal joint (coupling) will also be subject to more strain as it will not move as easily.

If you look at the diagram in this thread, you will see at least 4 places on the steering column where joints will be at an increased strain (stress) due to lack of power assist.
http://www.contour.org/ubbthreads/showflat.php?Cat=&Board=trouble&Number=1250417&fpart=1&PHPSESSID=