Question:  

Is this meter accurate enough - and/or - will this meter read a low enough value?

Answer:  

There is a general measurement principle that for accurate measurement, the measuring device should have a resolution that is ten times more than the required reading.
For example, to accurately measure to 1 cm a ruler should resolve (show) 1 mm. 
In practical terms the this can be also four times more but on digital meters the resolution steps in factors of ten.

As an example the lowest range on a particular meter is 320.0 mV (resolving to 0.1 mV) the lowest value any randomly selected one of those meters should be used to accurately measure is 1 mV. 
It can be used to indicate values below 1 mV but how that reading is used determines if the tolerance on the reading is acceptable.

Using a specific value of 0.5 mV, the accuracy specification calculates to  ±0.1 mV, how that value is being used would determine how relevant it is. 
In reality it is measuring an “unknown” value of a nominal 0.5 mV but the meter can only show 0.4 mV or 0.5 mV or 0.6 mV, which is a deviation of 20%.