Is a VHF NAV receiver inherently capable of processing a LOC signal?
Any VHF radio can receive the carrier signal of a LOC signal but to use it, you need dedicated circuitry.

The LOC transmitter transmits the carrier wave, frequency modulated with two side lobes of 90Hz and 150Hz.  In order to use the LOC signal, circuitry needs to exist which will filter out the 90 and 150Hz then measure the difference between them to determine where in the beam the receiver is located.

This circuitry is dedicated to the ILS receiver. 

It's a similar story for GS which simply uses lobes above each other, rather than left and right.

So


  Is LOC signal processing an inherent capability of a NAV receiver


No.


  Are there NAV receivers incapable of LOC signal processing.


Yes.  All of them which do not have an ILS function (e.g. the Rockwell Collins VOR-900).

[ BEGIN Mythbusters Territory]

I've just tuned my hand held airband receiver to the ILS of my local airport.  I think I can make out the beat frequencies from the 90 and 150Hz although I doubt that the low pass filter is letting much 90Hz through.  I guess it's optimised for voice reception so probably cuts off at about 100 or 120Hz.

The next time I drive past the end of the runway, I'm going to test whether I can detect any change in the beat frequencies as I drive through the lobes.  There is a convenient hill about a mile from the threshold which will put me a couple of hundred feet above so I should be in the beam.

I guess it might just be plausible to hear when you are going left and right of the centre line.

I'll report back.

[END Mythbusters Territory]