On the principle it is a good idea. But in practice, I see a big drawback. First is the lack of precision, as the gas within the bag may not be homogeneous and you will have eratic readings... It may be dangerous to compress an unknown gas (O2 in excess of 40%) considering that your analysis may not be precise. Imagine that your HE hose disconnect or He bank is empty and your O2 % will immediately raise over 40%.... I am not certain how you plan to inject air inside, depending of the method it may not be very accurate.... I have a small compressor and the inspiration is varying along a tank filling. You need to have a way to tune the air, o2 or He entry along the blending.
I would rather avoid compressing O2 if a proper "mixing" is not made before.

I suggest to use this method for Helium only. As for O2, do it separately by partial pressure (lyre) with a O2 clean tank. Or you can buy a Continious Blending mixer, that will mix properly the gas before entering the compressor. Make sure to have an analyser before the compressor to do not exceed the 40%. To buy a mixer you can do it in France at Bigata.fr or underwaterexplorers in Bordeaux. Buy it in Europe, in US it is incredibly expensive as a company registered a patent...