I don't know what you mean by a "Texas" tomato cage, but yes, any fence type structure is fine for peas. I used regular tomato cages one time for sugar snaps, which was OK until they started to produce pods, the vines grew far taller than the cages, and then they flopped. Lesson learned -- just make sure the size of the support matches the potential height of the variety you grows. Regular tomato cages are fine for short peas, it takes something taller for a taller pea. I'm guessing that "Texas" tomato cages are big and tall?

Go for it! I use normal tomatoe cages for my snap peas. They work great. IIRC Texas tomato cages are real tall. They'll do just fine!

Yep, that is what I do.

Great. I spent a bundle on those cages; love 'em, but I want to get my $ worth.

I'd try it. you have nothing to lose. I mistakenly didn't give my peas enough support in the spring and it turned into a mess. I find every variety I select grows 5-6 feet tall. Support with give you many more peas and keep things clean.