Current NROTC instructor here. I'll answer your initial question and some of the others that came up in the thread:
1. Yes, you can take summer courses. We have mids every summer who do it. We have them work the courses around their summer cruises and haven't had a conflict yet. The only cruise that has "set" dates is CORTRAMID, between your freshmen and sophomore years. And even that can be flexible - we've sent mids to CORTRAMID West (with different dates) to accommodate their summer school requests.
2. Responding to Python - yes, only first class cruise is required. However, (and this depends on the unit culture and CO's guidance), in our unit it would be a rare case where a mid misses a cruise opportunity for class. There are just too many options, with colleges offering multiple sessions, for a cruise not to work out.
3. The unit may actually pay for it - it all depends on your major and why you're taking courses over the summer. The CO has a lot of flexibility in this regard, and some grant summer benefits more liberally than others.
4. I haven't seen "extended benefits" - paying for additional semesters - work out favorably. Usually we place the mid on leave of absence, which means you continue in the program but the Navy doesn't pay your tuition.
One of the first things you'll do in the program is develop a "degree completion plan" with your class advisor. It'll have all of the courses you need (geneds, major and NROTC) to finish spread out over four years. With it, you can have an immediate tentative plan of how many courses you need to graduate and whether or not summer school is required.
That said, we have plenty of physics majors who don't need extra time. I guess it all depends on how many courses you transfer in. Hope this helps, and I'm happy to answer more of your questions if you have them.