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The answer is no.

The X5's built-in tuner is a simple chromatic one with fixed reference pitch at 440 HZ and no alternative tunings (drop/capo etc) unlike the features available on the PolyTune.

 
There is unlikely to be any change to this arrangement as a conscious decision was made to create a very DSP efficient version of the tuner, so that it can run on top of the FX without it hijacking 1 of the 5 slots or limiting the load of certain process-heavy pedal combinations.