Engineman1 writes:

Am I
correct in assuming that if the flowmeter is set to read say, 5 liters
per second in each case, the actual gas output will be about 10 times
as much with the direct connection?

If you mean a rotameter (what it sounds like you are describing) these read
volumetric flowrate at standard conditions (volumes of gas at 14.7 psia and
70 deg F). So no, you would not be at all correct with that factor of 10.

Also, your meter is calibrated for oxygen, and you must also correct
proportionately for the different molecular weight of propane. (Assuming
you have pure propane--I hear it sometimes has a butane fraction.)