Effects of averaged periodogram (Welch's Method) on resolution?
Yes, if you reduce the FFT window from 4096 to 1024 samples, then you will have 4 times less frequency resolution. Also, if you have significant overlap between the windows, your resolution will not change. It only depends on the length of the FFT window. Furthermore, with Welch's method, a window for each segment is usually used, which again reduces the spectral resolution due to convolution of the signal spectrum with the window spectrum. 

So, yes Welch's method reduces noise, but also spectral resolution. 

If you want to have both, why dont you increase the recorded signal length to lets say 4*4096? This would amount to 360ms, which, depending on your requirements, might still be fine for guitar pitch detection. THere's always the tradeoff between spectral resolution and required amount of time.