Sounds sound. There is a design feature you might need to include. That is a "vacuum breaker" which is a modified check valve to a vent. This will allow fluid from the overhead pipe to return both to the drain and some to the sump - no problem. This prevents possible syphoning of water in your drain uncontrolled into the garage in case of a power failure - not recommended. You might be tempted to just include a forward check valve in series. I recommend against this as due to Murphy et al., it will fail when least desirable.