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I understand that when a Single Photon Avalanche Diode (SPAD) is biased and a photon hits it, an avalanche process is activated that cause a current. What happens if two photons hit it? Will the process be more intense and there will be a proportionally higher current? Or is it simply either on or off? I'm trying to figure out the advantage of an Silicon Photomultiplier (SiPM) comparing to a single SPAD with a high gain. I had a suspicion that this might be one.

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An SiPM is just an array of SPADs whose outputs are summed. A SPAD is just an Avalanche Photodiode operated in Geiger mode (like a Geiger-Muller tube) where any detectable signal produces the same sized avalanche output. So yes, a SPAD does produce a "digital" on/off signal that is same size whether one or two or more photons hit it simultaneously. As long as multiple simultaneous photons hit different SPAD pixels in a SiPM, the output of the SiPM will be proportional to the number of photons.

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