Unless there is a floating gear in a gear transmission system, the degree of freedom of gear systems is zero, that is, a gear system can be considered as one single rigid body, hence they are linear. However, there are clearances, tolerances between the gears and in other connections in the gear system. These small clearances can cause some small non-linearities, but they can be significant only at very high speeds. But also these small nonlinearities at higher speeds may also cause the system results in failing. Between the engine and PTO, the rigidity is more (more linearity) than that between the engine and the wheels because of more joints and gears between the engine and the wheels.
Hydraulic system is usually nonlinear except at very very low speeds. But at higher speeds, hydraulic systems usually nonlinear, even chaotic sometimes.
As for at which speed of PTO should run when pulling an attachment; usually 540 rpm of PTO is designed to get the designed speed at the blades. But the blade speed can not be theoretical, - must be an emphirically designed speed. That is, many experiments on many different grass types are made and from the data collected, an average blade speed is determined. According to this average blade speed, the gear system is designed to connect to 540 rpm of PTO. Tolerances are given to the gear system to cover different grasses which are tested before. If your grass type deviates much from the tested grasses by designers, then you can run your PTO at another speed to obtain proper speed at the blade for your special grass.