Just try it. Mooshimeter has quite good resolution for amps and should be able to show even much smaller differences.

Specs state that it should be possible to see “Less than 5 µA per count in 10 Amp scale”:
https://moosh.im/mooshimeter/specs/

As a post from yesterday was about feature request for math channel(s) for mooshi-app, this is also something that we could do with it.. After little head scratching you could have your 4-20 mA shown in percent or actual pressure or whatever you are measuring. That would be nice.

If you still need better resolution, you could use “aux” input (about 1 volt maximum) with shunt resistor. Again, ability to do math on the fly would be really nice..