If you are talking about the US, no I don't think an education minor would really help that much. Better off spending that time adjunct teaching or TAing.
On the other hand, if you wanted to specialize in something like Physics Education in grad school, having some kind of education background in undergrad might help. I suspect that is the case, but I don't know.
My advice if you want to teach physics at the college level: Work hard, get good grades. Publish. Make sure you get some teaching experience in grad school. TA some courses, try to win a teaching award. Do a leave replacement job after graduation. Get good recs. Publish while teaching there - hard to do if you are an experimentalist, so maybe do some theory or simulation or something that is portable and cheap. At that point, you will probably start looking like a good candidate for a 4 year college position. Then all you need to do is apply to 50-60 job openings a year and a boatload of luck.
If you are instead targeting R1 universities, don't worry so much about the teaching. Just publish publish publish. The better the journal, the better off you'll be. Go to conferences and network. Get your name out. You will probably need more luck than in the 4 year college track. If you can prove that you are a genuine superstar, at this point, you will probably have a lot of options. There are generally fewer jobs at this level, and the competition is probably tougher. Also, the timing of your job hunt is also more important. If only 5-10 universities have programs in what you do, and none of them are hiring, then no job for you.
In short, have a backup plan. IF you make it as far as you think you will and IF you still want to be a prof at that point in time (2 big IF's), you still probably won't get a tenured-track position, just because. So have something else in mind 'just in case'.