All well and good, audioguru. Thank you.
But, if a string is plucked, in the tuning process, without any interference, and it is at precisely the note sought, it will resonant properly and without harmonics. I have been going on the assumption that the OP wished to use his counter for tuning purposes.
The counter will, of course, give wildly fluctuating readouts until the proper, single frequency for the key he is tuning for is reached. But once tuned correctly, it will display the right frequency, whether or not the signal to it is clipped.
Now, if the OP meant he wished to see whatever frequency(s) are being played, regardless of finger on string manipulations or plucking positions, then, yes, of course, the harmonics will abound and with or without the clipping effect of the preamp the counter will be over whelmed and display gibberish.
In the above example, I can't think of any situations where any counter could suffice for the OPs needs and equipment on hand. A spectrum analyzer, yes. But not a counter.