Yea, if you put the time in I think you could catch up rather quickly. To be completely honest, your chance of success depends 50% on your willingness to put in the time and 50% getting a decent professor in your classes.
Some university professors are quite unforgiving if you haven't mastered the previous semester, but most are willing to work with you.
I think HS education will make things easier for your first year or two in college, but if you're dedicated it won't hinder you as much as you'd think (if you dropped out).
Just realize that ANYTHING is possible if you're willing to work for it, so never get discouraged.
EDIT:
But if you're asking how long it would take to learn all of what you learned in HS? Probably a summer for the math and science. I've helped some people study for standardized tests for math and science, and they knew absolutely nothing from HS (not even simple algebra), and after a couple of weeks they were ready for the exam, up to and including precalc/trig/geom/alg. I think its a matter of getting over the intimidation and picking out what information is actually useful.