If there was a lot of bearing clearance in the mains, the rods
might run a little dry, for sure. The rods are fed oil through the
crank from the main bearings, and too little pressure might result in
most of it getting away at the main bearings. In some simpler engines
the oil is fed only into one end of the crank, and if the pressure is
low it will reach the first rod OK but can't fight centrifugal forces
back through crank axis to the next rod. I don't know of any aero
engines that are single-point fed, but there are plenty of industrial
engines like that.
The key to good rod and main bearing lubrication is
clearances as small as the manufacturer will allow, and this also
reduces oil consumption by keeping the cylinders as dry as possible.
(Cylinders are typically lubricated by oil flung off the main and rod
bearings.) The pistons and rings have relatively little pressure on
them and need very little oil. In any engine or compressor I've seen
that failed due to lack of lube, the bearings were always the first to
go.

Dan