Short answer: yes, you can train for a Sport Pilot license in a non-LSA plane, such as a C150 or 172. Yes, the hours count.
Long answer: bad idea for a couple of reasons.
1) One of the tricky bits about a Sport Pilot license is that every time you change class and type of aircraft you need another check ride. On the day of your check ride your license and log book will clear you for PIC with notation of class, type, and model of aircraft. That doesn't mean you can only fly the exact model of aircraft - if you're checked out in a CTLS you can fly any aircraft that matches it.
It does mean that even if the local FDSO signed off (okay'd you for) a check ride in a 150 and you passed you would be ineligible to fly ANY aircraft as PIC, as it is not an LSA. Crazy, ain't it? You can train and earn your license in a plane up until you are qualified to fly it competently - and the are instantly disqualified to assume the controls due to it not being an LSA.
For me this means that I'll have to pay for two check rides - the first in the trainer I'm learning in and then a second for when I finish my little Nieuport 11 replica (tail dragging biplane is quite different than a hot little CTLS).
2) The difference in the way a C172 behaves and a little LSA like the CTLS is pretty big (I've flown both). Hint: one is a lot more squirrely, particularly in gusts, crosswinds, thermals, etc., and it ain't the 172.
3) You're trying to absorb enough without having to learn to transition from one plane to another. Good grief, why pile it on?
4) I'm in the same boat, and have to drive an hour each way to get lessons from a good CFI in an LSA. Would I rather drive not ten minutes from my house instead? You betcha - but in the long run it's a better use of my time and money.
Isn't your sonex a two seater with dual controls? Why not train in it? Your instructor simply has to have five hours of his own stick time in it.....