Yes it does, but the number is so small I wouldn't worry about it. 22.6 mv into 8 ohms is 0.000064 watts!
This is an old thread but needs some correcting. The user who has -22 mV of offset on his amp needs a little clarification.
First, offset can be negative or positive. We would like it to be zero but 22 mv is quite acceptable. However when we connect a Zero to this,whose DC resistance is almost ZERO we can have significant current flowing which can saturate the core and make for some very bad bass and IM distortion. The impedance selected matters not.
The Zero is wound with very heavy wire and I do not know its DCR nor is that easy to measure with a DMM. Actually you measure low resistances by putting a known current throught the wire and seeing what the resultant voltage is. This is absoultely accurate and is not affected by probe resistances. Say the wire resistance was 0.2 ohms, which is quite likely then the current is 100 mA and I would expect quite a bit of core offset.