It's certainly "allowed" (you can even make same-day reservations if you want)...the big issue is whether there will be availability. At SSR, availability is there more than at most of the other resorts (that's also true for OKW), but
DVC is designed to be pretty much full all the time and most of the time it is...
Having said that, if you call and discover no availability, you can go on a wait/list, and/or you can call back each day...we've done several last minute trips ("lastest-minute" one we did was 5 days out; second-most was 12 days out--the first one was for the first week of January, over marathon weekend; the second for spring break)...each time after several phone calls we got five nights...the first time we had to move from OKW to SSR to BWV (Fri, Sat, Sun) where we then stayed for five days (that piece of the reservation had been made months earlier; it was the extra weekend that was last minute). The second time we got all five nights together in a one bedroom at OKW...another time we did a five-night one-bedroom--we also got OKW that time--with only 6 weeks lead-time. Again, it took a few phone calls, reserving nights as they came available, but we did wind up w/a "complete" reservation.
Now, we're in the midst of another such last-minute trip...this time, my DS (who's in college) told me about 2 months ahead of time that he wanted to go...we're bringing 3 of his friends (his grad present) and he REALLY wanted an Epcot resort...we got lucky (again, w/several phone calls and taking what was available and then filling in...we started w/the time at OKW, w/l'ed and got the OKW villa near HH; then moved to BCV as follows: the first two nights, w/the last 3 at OKW; then the last two nights w/an OKW night in the middle; then the last night came through...the W/L worked for the last (middle) night...the other two-day "chunks" came via me calling...this is for spring break week, too...Now, I want to add a studio (we're five adults in a one bedroom; I really would like that studio--for any if not all of the five nights!)...so far, no luck...but I'm restricted to BCV or BWV (the kids don't want me to move to another resort to which we can't walk; they'd rather crowd)...
So...bottom line (and long-winded answer): yes, you CAN make last-minute reservations--but it usually takes some patience and persistence and flexibility...
Good luck!