Well,
Given the above info, you should be on the right path.
Just getting the degree won't be enough to break in tho.
A bachelors level degree is what a high school diploma used to be,
You will need a good portfolio as well.
It also depends what your aspirations are?
Do you want to:
A. just be an artist in a team/ department?
B. Be an Art Director one day?
C. Be a creative director one day?
D. other? (specify)
Knowing the principles of programming, and some languages will help you if your goal is B or C, since you will need to know how to get your assets into the engine and get them working, it's all the better if you can do it all yourself, than have to wait on a coder to help you.
On my team, we combine creative and Art Director in one person, and he knows the entire pipeline for not just art, but all other assets.
If you can major in art, with a minor in programming, you would stand out above other artists in your class. (knowing programing in any regard will help you problem solve better)
I'm not sure if you understand how rare it is to have a fully competent person who knows and can produce art & code very well. My former project co-founder was one of those, but he came more from the Code side, and went to a tech school.
As for the networking diversity concern, it's valid, but don't think too much on it, your training to be a specialist, at a trade school, your bound to find those similar and different to you enough.
The question would be, what's your other options?