Jeff,
Gee lots of questions today, is someone getting close to going to API? Well, let's see, I don't think there is any hard and fast answer to this question, just a lot of opinions.
With regard to spending your own $$ to pursue a pilot's license while in college, well, there are definitely pros and cons to it, let me see if I can list them for you that come to mind:
Advantages:
becoming familiar with flight in general, gaining some experience and hours
familiar with landing and taking off, basic airwork, comms, etc.
possibly already soloed, give you more confidence prior to coming here
stronger understanding of VFR flight rules and procedures and aerodynamic principles
Disadvantages:
relearning many of the procedures the way the Navy wants you to fly
instructors may expect more from you based on how many flight hours you have accumulated, and grade you to a higher standard
T34 is a completely different aircraft, with different handling characteristics
Based on the number of flight hours that you have when you get to Primary, determines whether or not you are put on an accelerated program in the beginning of training, unfortunately I don't know what that cut off is, though I would imagine the instructor really has the most say in it on seeing you handle the plane for the first flight. Though I have heard instructors comment that they can't distinguish between two students (one with no flight experience, the other with lets say 200 hours) after they both have gone through training up to their solo flight. Of course there are those people out there that are just naturals, and pick up everything VERY quickly, but for the sake of this discussion I am discounting them.
My personal feeling is that if you have the opportunity to, and the $$ to spend on getting some flight time in college, go for it. If it is too expensive and you decide not to, no big deal, the program is designed to take those through with no previous flight experience (I am proof of that!). But just keep in mind that some of what you learn in civil aviation is not going to apply here in training, such as the landing pattern, and you may have to "forget some of what you have already learned". I don't really know how much that would affect you, seeing as how my first exposure flying was here at Primary.
But in the end, what you are most concerned about is doing well in the program, and I have noticed that students with previous flight hours tend to do better (grade wise) than the rest of us, and stand a better chance at the end of Primary of getting to fly the plane they want (of course I don't have an hard data to back this up with, just an opinion of mine from what I have seen so far). I did well in Primary, and finished with jet grades, and managed to get my first choice of P3s, so it is possible to do well here without any previous experience. But the definite keys to success, not just in Primary, is to study your procedures and be prepared for each of the hurdles that the program throws in front of you.