In short - yes, you can. This is because as long as the legs of the trampoline or, indeed, any other heavy object is not sharp, then the artificial grass will remain in a healthy condition. You should ensure, though, that the sub-base below the artificial grass surface has been properly installed to ensure there is no lasting indentation from where the trampoline has been sat over a prolonged period. A deeper subbase and thorough compaction will prevent this, even for things that are very heavy!
Should you decide to move the trampoline to another area of the garden or take it down completely, the artificial grass blades can be brushed back up using a regular brush. Your turf will look as new as the day it was first installed. The same also applies to other playground equipment, such as swings and seesaws, as well as garden furniture, such as tables, chairs, and benches. We would recommend that you move the object around the garden periodically, though. Alternatively, we would recommend using any offcuts you might have to put under the feet of the trampoline-making coasters (much like you would do with your sofa on an indoor carpet). This will make it easier to brush the grass back up after it has been compressed by the object.
If you would rather not have the trampoline standing on the artificial grass surface, then it is possible to sink the trampoline into the ground and lay the turf around it. Sinking the trampoline into the ground also takes away the need for a safety net, with the artificial turf (which is now at the same level as the trampoline) lending itself to a suitably cushioned fall.