Yes, the axles on a towed vehicle do count, at least in most cases. The ways vehicles are classified for toll purposes is far from uniform.
I don't think there is such a thing as an average cost across all toll roads, or at least not a useful one. The fees vary quite a bit, and in different proportions for different vehicle classes. Most toll roads do have toll calculators online if you search for them; for example,
here is the one for the New York Thruway.
In this particular case with the towed you'd presumably be a class 4H (four axles, tall vehicle), and the toll from Albany (exit B1) to the PA state line beyond Buffalo would be $65.70 cash or out of state EZ-pass. If you drove the motorhome and car separately, the tolls would be $34.75 + $17.60, or $52.35. If you have the NY state EZ-Pass with the Motorhome Thruway Plan, the toll (with the car in tow) would be $30.54. If you don't have an EZ-pass transponder already and are planning on going through New York, it is in my opinion well worth considering this latter option, for rather obvious reasons.