I got one back in, oh... Eighth grade? I only ever had issues with it for tests like the SAT, ACT, and AP exams. Never for anything within my school.
The CX CAS is exactly the same thing as the CX, but it has special software that lets it handle symbolic work, like simplifying expressions and solving arbitrary equations. If their only requirement is that they can clear its memory, and they allow the CX, then they'll allow the CX CAS.
That being said, I don't recommend it. It's super overpriced (even at the price of a Ti-84, it's just a fact about all those graphing calculators), its interface is awkward (it has a cheap/shoddy trackpad for navigation, its keyboard is alphabetical, and it loves its software drop-down menus), and the CAS won't help you in the long run.
It does have a 3D graphing feature, which is cool. But no matter how hard it tries, its 20-year-old, low-power, 135MHz CPU can't quite handle it.
I lost mine after a year or so, then got a TI-36X Pro. I thought I was getting a downgrade, but that's actually the best calculator I've ever used, and I'm still using it three years into a math degree. I have a TI-84, but I haven't touched it in years.
If you could buy it, use it for the test, then sell it for a profit ('cause you said it's discounted), then I say go for it since they'll probably allow it. But if not, I actually wouldn't recommend a TI graphing calculator at all. If you need a graphing calculator, then it's better than the rest of the lineup, but that's not saying much.
I've spoilered the last portion since it ended up being a rant. Needless to say, I have my personal biases.
There is utility in being able to use the 'shortcuts' afforded by the CAS software, but in high school the things it skips over are exactly what you're supposed to be learning how to do. Once you get to the higher levels, 9 times out of 10 you should be able to do the work yourself faster than it would take to type it into the calculator and wait for it to give you an answer.
It really does boggle my mind that their sole purpose is as educational tools. They're basically just slow "do it for me" machines that keep you from learning what you need to early on then give you no actual utility later. The only way they're a good thing for education is if the goal is to push kids through k-12 as quickly and as quietly as possible, rather than making them actually learn something.
And it's not even like TI cares about making them useful anyway. The TI-84 is still $100 and it's so antiquated I'd be willing to bet there've been more technologically sophisticated McDonald's toys. Blegh.