Most likely the school you transfer to will want to monitor you for a semester or two while you are in the unit as a midshipman with no scholarship. There are a couple of ways to pick up a scholarship, and one of the easiest is sometimes the CO has the authority to "grant" one or two a year. He/She will usually pick the midshipman with the best grades and most volunteer hours for the unit.
I showed up to Purdue without a scholarship, joined NROTC, and signed my 3 year papers after freshman year. But I was a fully integrated midshipman from day one on campus. I volunteered for all the extra duties we did to make money for the unit (Football security, ushering concerts on campus, etc) and participated in the Midshipman Big Brother program we had for some neighboring elementary schools.
As a bonus, if you need (or want) extra school time... it gives you a little leverage when you are asking for an extra semester or two on the back end of college. Although I only had a three year scholarship, I put in the paperwork and they paid for my 9th semester... the fact that they only had three years of tuition invested in me (I was told by my CO) was a large part of why my extra semester was so easily approved.