Is it possible...

to set it, to when you Prowl, that a seperate ActionBar comes up? Just like how it does for a Rogue when they stealth.

Would it be possible to make a macro for it?
You can do it with bartender, but you really don't need it. There's a grand total of 2 ability's that use stealth.
Yes it is.

#showtooltip
/cast Prowl
/swapactionbar 1 4 (Let's say 4 is the actionpage you want it to go to.)

Then, what ever opener you use, other than feral charge, will have this:

#showtooltip
/cast (Whichever opener)
/swapactionbar 4 1

Now why we would ever need this, it is beyond me. We have two stealth required spells.
It's not necessary to swap action bars. You can macro your spells using the [stealth] and [nostealth] conditions.

Example:
/cast [stealth] Ravage; [nostealth] Mangle(Cat Form)
Mine does it automatically. I never set it up. It drives me nuts. I had to put normal abilities into the stealth bar just incase I needed them. i.e. Dash