In Search of Voice Activity Detection Algorithms - What happens to the frequency or pitch or speech features as speaker moves away from microphone
The intrinsic fundamental frequency (pitch) of a speech signal do not change when the speaker moves away from the microphone (unless it moves away quite fast in which case it's a case of Doppler effect!) - it would be strange if we heard people's voice transposed up or down as they move away or as ambient noise increases!

However, as the distance from the microphone increases, the signal to noise ratio will increase, and this might affect the reliability of a naive pitch detector, so you might indeed get different result when estimating the f0 of a speech signal and the same signal with more noise. It doesn't mean that the f0 is different, just that the noise makes the estimate unreliable.

I am not aware of any naive feature which allows noise-robust speech/non-speech discrimination with a simple threshold rule. I think supervised machine learning would be the way to go for your problem.