The information I have found so far tells me that the bypass is required. Mostly from tech info about industrial centrifugal pump applications where the pump is "deadheaded" (like a car engine when the t-stat is closed). In a car, the bypass allows the coolant to temperature to "even out" though the engine because there is (bypass) re circulation when the t-stat is closed.
The bypass also allows the pump to provide minimum flow under deadheaded conditions which reduces cavitation and pump failure (pump is churning water without flow). This is from an industrial site:
In order to ensure adequate cooling and lubrication of the pump, there must be sufficient volume flow through the pump. Inadequate cooling and lubrication leads to overheating, bearing wear, friction between the sealing faces, leaks at the shaft seal, all of which will lead to pump malfunctions or failures. This is why a bypass line needs to be installed if there is a risk that the pump cannot be operated at the necessary minimum flow rate.
The bypass line is to be drawn from the pump's vent port or the discharge pipe's vent port, either back to the suction side (if possible) or into a tank, in order to ensure sufficient cooling by the pumped medium. On return, it must be possible for the pumped medium to cool down before it is fed back into the pump in order to avoid overheating the pump. For this reason, the bypass line must never be connected directly to the pump's suction port. The bypass line has been configured correctly if the minimum flow rate requirements for the respective pump as specified in the operating instructions have been fulfilled. At full load, the volume flowing through the system and the bypass may not exceed the maximum flow rate delivered by the pump.