The rack should be fine from running empty. It does lubricate the internals of the rack but even if not pressurize you'd probably still have some residual fluid in the housing.
The stock power steering pumps tend to get noisy on the 2.4L, especially if you haven't regularly changed the ATF+4 fluid. Running a power steering pump dry can cause bearing and internal wear but your first course of action is to find where the fluid went. Maybe the reservoir cracked. Maybe a line rusted or broke. Maybe the rack is leaking internally out the tie rod boots.
Get that fixed, refill the system and see if there's any noise or problems. If there's been some noise/whine and you think it might be a little worse after fixing the source of the leak, I'd consider using a syringe or something to occasionally pull a little ATF+4 fluid out of the reservoir to make sure there's no metal or other debris.
Eric H. - '04 Neon SRT-4 (eBlue/S2) - '92 Dodge Daytona IROC R/T
'91 Dodge Spirit R/T - '19 Pacifica Hybrid Limited - '14 CTS-V Wagon
'08 Cobalt SS Turbo - '14 Cruze Turbo Diesel - '02 SVT Focus (S/C)
'04 SVT Focus (EAP) - '07 Ram 1500 - '81 & '85 Chevy Citation X-11
'90 Pontiac Turbo Gran Prix (ASC/McLaren) - '93 Olds Achieva SCX W41