Does the FFT size matter in OFDM demodulation?

What is the impact of taking an arbitrary larger FFT size during the demodulation process?

It doesn't work.

This gets pretty intuitive if you take an arbitrary OFDM introduction and look at the spectrum of OFDM, consisting of overlapping sinc functions: you need to hit exactly that raster, or you don't see the individual channels, but an undisambiguable mishmash of carriers.

Using a larger FFT at the same sample rate can't work: don't forget that the FFT is just a DFT. A DFT maps vectors of a specific length N from time domain to frequency domain vectors of exactly the same size. So, a larger FFT length simply needs more time domain samples. But your OFDM symbol is as as many samples long as the transmit FFT was.

So, no, you can't use any other FFT size, sensibly.

You'd have to increase the sample rate by the same integer factor that you've increased the FFT size.

But that would only yield an FFT where all but the original bins are only noise, so you'd have won nothing.

(This is actually done in some OFDM systems to have more headroom for frequency synchronization, but it's not desirable if you don't have a frequency offset larger than your outer guard carriers.)