Is it possible to damage a pneumatic pump/motor by applying too much pressure?
No, it would be practically impossible to damage LEGO pneumatic elements by overpressurizing them.



It turns out that LEGO pneumatic pumps actually have a very simple "slip" mechanism that prevents overpressurization.  Once the pressure reaches about 35-40psi (the exact threshold varies slightly pump by pump) the rubber plunger disk will give way and bend back, allowing a small amount of air to slip by and escape out the top of the pump.

Here is a GIF illustrating the effect, watch the rubber plunger disk bend back as I pump it:



Sorry the quality is so bad, it's hard getting under SE's 2MB limit.  The number markings on the pressure gauge are multiples of 10, so it is slipping at around 37psi.

If you don't have a transparent pump or a pressure gauge it is still quite easy to tell that this is happening since the air escaping makes a fairly obvious pfft sound.



Some have also correctly pointed out that the tubes will pop off long before any damage is done to the components.  While I have experienced this, the pump will usually hit its max pressure before any pipes pop off if they are attached securely (i.e. pushed as far as possible onto their connections).

Some pipes also tend to come off easier than others, in my experience the older ones along with the clear types tend to make looser connections.  This is why I try to use the newer opaque tubes first since it can be a pain in the neck fixing and repressurizing when a connection blows off.