God no.
Here's how the process works:
4/C and 3/C years: work out (on own volition) with SEALs on the yard, gather knowledge, make sure you have a good order of merit, and generally demonstrate interest.
2/C year: Participate in SEAL screener in either fall or spring. The screener is basically a haze-fest on constant (hard!) PT from a Friday afternoon through Sunday. They rank everyone who finishes (something like 90 started and 20-something finished this fall) based on performance and the top few get offered SEAL cruises. NROTC people come up the USNA to do the screener and generally all get smoked.
2/C-1/C summer: Go on a SEAL cruise. The first few days are like a mini-Hell Week, apparently several people dropped this summer. The rest of the time you work, train, and hang out with SEALs. Again, they rank everyone who finishes and this is taken into consideration at service selection.
1/C fall: Put SEALs first at service selection. Everyone who goes up for SEALs is interviewed. The interviews can be rough; any sticky spots on your record will be thoroughly discussed.
Late-1/C Fall: Hopefully, get SEALs! 28 got SEALs from my class. (SEALs/EOD, Med Corps, and Subs are the only communities to get informed early).
1/C Spring: SEAL practicum class*, keep training for BUD/S, pick BUD/S start date.
Post-Graduation: Go to BUD/S, start SEAL pipeline.
*Practicum is a class that all firsties take that's relevant to their service selection and just gives them helpful knowledge and training for after graduation. So, SWOs practice charts/mo boards and shiphandling, pilots learn the basic stuff you learn down in flight school, Marines learn Marine history, uniform wear, and do stuff like land nav. I'm not sure exactly what SEALs do, but I'd imagine they start learning the skills they need for BUD/S: pool competency stuff, dive physics, etc.