Aye it can and does.
This from a hydralic ram side of things with earth movers and diggers.
If its old fluid it will have a fair bit of water in it which will boil and cause cavitation in the pumps. which knackars them pretty quickly. If it really gets hot you will start melting seals.
Hydralic fluid is dangeous stuff when hot it sticks to you like nepalm and has quite a large heat capacity. I was never brave enough to do the last couple of threads of the tank plug with my fingers and try and snatch the plug from dropping in the 50 gallon drum.
From a flying side of things I have had a pump explode in the hot section dumping the entire lot in there and thankfully it didn't go on fire. Produced vast quantities of smoke though.