I had a GC2400 without loaded tires for 3 years, and now a GC1720 for 1 year with loaded tires (rimguard). I use(d) both as my primary mower for a 1.5 acre suburban residential lot. Haven't noticed any negatives with the loaded tires. Your mileage may vary depending how soft the ground is in your area. I suspect the extra weight would really start to be noticeable on any tractor larger than a SCUT, as the starting weight is already higher, and the tires bigger (capable of holding more ballast).
Bottom line, I would recommend loading your tires, use rim guard.
Edit:Never mind, I reread your profile, you're not talking about your GC1710. Not clear to me what you're doing with that potential 1758, but the result is likely still the same, recommend loading.