If the SNR is limited by reflections in the room, and the impulse response of the channel from the source to a specific microphone is unknown, then the received signal can be used to determine the impulse response of the channel (together with a known transmitter signal that is spectrally rich in content) and with that equalize the received signal. However 200 samples would likely be far too insufficient for this purpose. In channel equalization we are basically solving for inverse convolution a system of overdetermined equations such that each output (sample) represents a sum of prior samples with unknown weights (which we solve for). These prior samples must extend over the significant duration of the channel impulse response, and then we need several samples to determine a least squared solution: each new sample provides us a new equation, and we would like to have more equations than unknowns as the accuracy of the solution will be improved the more equations we can use -- up to the limits of assumed stationarity in the channel statistics (the channel will change with time, so up to a point further inputs will contribute no further improvement, and then it will actually degrade the result).
200 samples at 48 KSps is only 4.16 ms. I believe typical channel impulse responses for a small room can be in the 100's of ms but I am less familiar with audio engineering to have confidence in that. But to equalize the channel to improve SNR by eliminating reflections/reverb I would recommend determining the impulse response time of the channel and then using at least 5 times more samples than that for the channel estimation with a known spectrally rich signal (white noise such as a maximum length sequence or frequency chirp). The equalization filter itself once the coefficients are determined would be the length of the channel response.
Once all channels are equalized for each microphone, assuming the remaining background noise is white and uncorrelated, further SNR improvement can be gained by coherently summing the microphone outputs: align their delay and sum each signal weighted by the SNR for that microphone for optimal ratio combining. If all microphones have the same SNR, this will provide a $\sqrt{N}$ SNR improvement where $N$ is the number of microphones.
If SNR is not limited by reflections in the room or other coherent sources, then any number of samples from multiple microphones can be added to get the $\sqrt{N}$ SNR gain assuming the coherent signals are aligned and the noise is uncorrelated on each microphone.
