The TW motor does have an oil pump.
But the oil pump in our motors essentially only supplies FORCED oil to the cam bearings and rocker arms. The rest of the motor is almost totally either splash-oiled (piston skirt, piston pin, cylinder wall, etc.) or rotationally lubricated by "dipping" into oil stored in the crankcase ( Main bearings, connecting rod big end, transmission gears, timing chain, clutch).
Therefore a cooler is not interrupting a "main artery" as it would be on some automotive or motorcycle oil systems. Most of these circulate high-pressure oil (60-100+ PSI) forced through crankshaft and cam journals to babbit bearings with tight tolerances. Essentially they force oil through every moving part in the engine before returning it to the crankcase. Because the TW and many small engines use roller or ball bearings and splash oiling the TW pump puts out very little pressure because it is not needed. In fact it's usually less than 10psi at WOT.
The top end can only flow so much of the oil available from the pump at one time and the excess from the pump is bypassed to the crankcase on a continual basis.
Oil cooler covers designed to connect to a cooler reroute this bypass oil to a cooler on its way back to the crankcase.