Mixing analog reads with raw port reads
What you are trying to do is perfectly safe. In fact, you reading PINC
will have no effect whatsoever on the input circuitry. You are just
reading an I/O register and, whether you read it or not, this register
is updated on every clock cycle from a set of comparators that monitor
the pin voltages.

Just for completeness, I should mention that it is possible to disable
the comparators that update the register. The Atmel datasheet recommends
to disable them if you want the lowest possible ADC noise. If you follow
that recommendation, then reading PINC will just return zero. The
Arduino core library does not disable them: the input comparators are
thus always active, and you can get a meaningful value by reading that
digital input register.

Edit: You can selectivly disable the input comparator on the pin
A2 by issuing DIDR0 |= _BV(ADC2D);. But that is only useful if you
really need to maximize the accuracy.