I'll leave it to others to comment on how the wax rings compress, but I will offer comment on the seal.
As long as the combined height of the wax seals is greater than the gap between the toilet and the flange you should be OK, but I think it would have been better to place both wax ring together on the flange. That way you know that the wax rings were lined up when they came together. I think a #1 wax ring is about 1/2" thick, so with two you should be OK as far as total thickness.
The wax ring seals against water leaks and it also provides an airtight seal to keep sewer gases out. With that in mind you might be able to test the air seal if you did not caulk all the way around the base of the toilet. I'm not sure how useful the method is, but it may help. Did you notice any odor from the open closet flange when you had the toilet off? You can try to test to see if the wax ring has an airtight seal if you have a number of exhaust fans in the house. Close all exterior doors and windows, turn on your range hood if you have one, turn on you clothes drier to air dry only if you have one, and turn on any bathroom exhaust fans if you have them. The negative pressure caused by the exhaust fans will draw air into the house from a number of places including any open sewer vents. Go back to that new toilet install. If you smell sewer gases coming out from under the toilet then you do not have an airtight seal between the flange and the toilet. As always YMMV.
What made me think of this method is that one time I was installing a new toilet and I was working with my face close to the bowl. My wife turned on the clothes dryer and air started flow from the DWV to the empty toilet bowl. It wasn't exactly a spring breeze coming from there.