We have a hydraulic operated press which has a 5ft bed by about 3.5ft deep. So yes hydraulics can operate a clicker press. The hydraulic rams are at least 6" diameter if not 8". They look like overgrown 1 gal paint cans. The stop mechanism is a complex chain mechanism which controls the depth of strike. If you are off by a few thousanths it 'embeds' the steel rule in the top striker plate. Sometimes it gets a little touchy by itself as if the stop did not react fast enough.
Your biggest problem will be stopping the hyrdraulic piston at the right location (if you automate it). Hand pumping it will be a pain!
Overall, yes hydraulic units can be used but they need to be controlled carefully. We also have the swingarm style. Ours seem to adjust very well without many problems considering their age.