If the ZTR is commercial grade, I wouldn't be concerned. If its not, I would be.
One thing to check would be to see if the ZTR has a bagger kit available from Deere. If they will sell a bagger kit for the mower from the OEM, then the hydro's could likely handle the extra weight and strain. On the other hand, if it doesn't, I would proceed cautiously as I was at my buddy's shop yesterday who I buy my ExMark from and he showed me repairing the hydro's on one machine, the bill was nearly $5,500 and only $600 of that was labor, the hydro parts prices have gone through the roof.
Plus, the time to get them is crazy slow. He has one machine which has been down now 10 weeks waiting for hydro parts..........Even though the machine brands are different, many use the same engines and hydro's, so be careful about possibly damaging yours.........
When you add a bagger to the Zero turns, it requires adding front ballast, plus the weight of the material collection system itself. If the machine can handle the weight from the factory, then I wouldn't be as concerned about using the cyclone rake behind it. I happened to read the Operators Manual for the MCS for my ExMark on Sunday and the MCS system and counter weights and deck blower weigh a combined 460 pounds when installed. I thought that sounded crazy, until I put the MCS system on it myself..............