The real problem with slicks on the road will be a couple of things. The compound for these heat cycle out extremely quickly(30ish cycles). The sidewalls are so soft, that in order to actually get around town without de-beading, or without severely damaging your wheels, you have to run a pressure in it so high that it effectively ruins the center groove on the slicks. Which will be the most important when you take it to the drag strip. So, they'll be really hard, and all the good compound will be gone.
Another issue you will notice, if this will is your first time on them, will be how severely out of balance they are and how noticeably they deform or 'runout' as the speed gets faster. If its a taller side wall slick, the runout can expand the overall diameter from 24.5 to 25-26 depending on the tire. The runout for every bias ply slick will be stamped on the sidewall somewhere, you'll also wan't to check to make sure they match side to side. I had an issue once with almost hitting a wall at 140+.
You cant account for the deformation with static or dynamic wheel balancing to counter it out because at different speeds, the weights would have to move. So we just leave them unbalanced.
If possible, you'll want to store them inside. A trick I use is to spray them down with my 'Special Sauce' (lol... oh yeah!) then wrap the surface many times with saran wrap. If its going to be an organized street race though(which I'm not condoning

), I would certainly use them. The difference in traction is phenomenal. What about drag radials for the street?