It'll depend more on how your AFROTC instructors feel than your coaches, especially if you're on scholarship. I do Army ROTC and just completed my freshman year with a scholarship and if knew a lot of people in my program and other programs that did it. We even have a 1:52 800/2:25 1k guy that's in his junior year. We also had a crew guy, football guy, and a couple of rugby players. Other schools had guys and girls playing soccer, diving, squash, etc as varsity members. When you're receiving your branch for your future career, sports/club participation adds a little bit to the overall package along with GPA and such as a factor for whether you get your first choice of branch or your third or fourth choice.
However you will need to realize that AFROTC comes first, I'm not familiar with how much weekend training you do but you might have to miss some meets. On the flip side you might not have to go to 6:00am PT because you get the proper exercise through track and xc. If you can't perform at a high level with push ups and sit ups though then you'll be pulled into doing both. So do your push ups. Just do them.
Once you start applying to schools, talk to the AFROTC instructors and find out what they think of doing sports and ROTC. Talk to the coaches too so they know that you'll have a bigger commitment from the get go. Best of luck as you apply for the scholarship and everything! Keep up on running, if you can run well in the military then you'll garner a decent amount of initial respect.