There a three types of PTO's.
1. Transmission driven. Tractor has a single disc clutch, Transmission and PTO start and stop together. Example N series Ford, older Farmnones, A, B, C, H, M etc, John Deere 2 cylinders before 1953 even some after, AC B, C, etc, Ferguson TO20 and TO30, almost all Massey Harris, most all tractors built before 1950, and a lot of early imports. These MUST have an over running clutch. Although a lot of aftermarket companies made a clutch that went on the differential and opened the drive to the rear wheels so the PTO could start before the transmission, this made the tractor more or less the same as a live PTO.
2 Live PTO Tractors with 2 stage clutch, 1/2 down stops transmission, complete down stops PTO, 1/2 way up starts PTO, complete up drives transmission. No need for an over running clutch as most have no brake.
3 Independant PTO Totally separate from the transmission. Controlled by a separate clutch, may be hand, or hydraulically engaged. If hydraulically engaged, you may engage by a lever-controlled valve or if electrically engaged you turn a knob or move a switch. Most of these have a brake to stop rotation when turned off. Some will NOT engage brake until the lever is moved far enough to apply it. Check your operator manual to check for operation, it should tell you if you if and when the brake is applied. If the brake is controllable, you don't need an over running clutch.
Most over running clutches that I am familiar with are mounted on the tractor PTO shaft therefore extend the shafts length and may be more likely to be bent or hit from something, it is possible it could cause a vibration or become out of balance. Most of the better quality and more expensive equipment that need them have over running clutches "built in". Rotary mowers though usually do no, and would need them the most.