Agree that this is not the right tool for the job, however for slightly different reasons. Polarisation is what the EE world usually call bias. For your application this would appear as a voltage source in series with the ammeter. Set it to zero and you could ignore it.
However, this instrument is intended to measure differences in current, not absolute current, and to maximise resolution it limits the dynamic range. For your application, I would guess that an absolute measurement would be wanted. The uCurrent fits this bill. Another option could be member Gyro's picoammeter project.
Lastly, is the question of what exactly you are measuring. If you just want to measure the minimum current then any of the above options could work. However if you want to estimate battery life i.e. total energy used, and you device is a type which mostly sleeps then occasionally wakes up with mA plus currents, then the above tools probably won't have enough dynamic range. It's possible to work around this by measuring the peaks separately (using a 'scope) and then manually adding the two contributions, but if you want a single instrument to do this for you then you need something equivalent to the rather pricy joulescope, or the more reasonably priced Nordic RF power profiler.