Certified mail (with return receipt) means that someone will have to sign for it from the mailman when it reaches the destination. Thus, there is an actual signature and date stamped on the return receipt. Also, the other certified mail receipt will have the date and time stamped at the post office when you send it. So it doesn't matter if the admissions office lost it or not, when you show proof to the school that you sent the check by the deadline and have a signature showing it was received, then the school must honor it and surely will since they know it was their fault.
Your other scenario (unless done weeks before deadline) can screw you. What if you sent it by regular mail days before the deadline and then when you call the following week (after the deadline), they say they never received it and your spot has been given to someone else. They also ask why you never sent it by certified mail. Whatcha gonna do?