The Big Ten rate code is only applicable to the employees of those universities (plus possibly the CIC schools, which adds Chicago). The chances of checking for ID aren't large; I've been asked a handful of times in all of my rentals, including maybe once or twice at MCO. Though, I think Michigan has a separately negotiated rate with National, because I use a different code than the "regular" B1G one.
But, the real problem is what happens if something goes wrong with the car. If this is the same rate I use, it includes LDW; the LDW coverage can't be waived. But, in following up on any damage, the fact that neither you nor your spouse are a B1G employee is likely to come up. That will void the LDW coverage. Worse, if you have the usual credit card coverage, that won't apply either, because those plans typically require that you *waive* the rental company's coverage.
So, the bottom line is to be ABSOLUTELY SURE that you have other *primary* coverage that is in effect when renting under a code to which you are not entitled. Either that, or drive very very carefully...