Right. There's certainly no way to be certain that you'll see every coupon after a certain number of steps, since for any finite k it's possible (albeit increasingly unlikely) that you'll just get k copies of the same coupon in the first k steps.
On the other hand, the problem of determining the expected value of how long this would take is called the Coupon Collector's Problem. Shockingly, neither Wolfram nor Wikipedia has anything more than a cursory statement of the problem, but if memory serves me right, it comes out to roughly N * ln(N) as the expected number of tries to get all N coupons. I don't know what the standard deviation is, however, so I'm not sure how you'd calculate the 95% or 99% confidence thresholds.
I'm sure you should be able to find some resources out there, though, now that you've got the name of the problem.