[I'm no microbiology expert, so obviously take this with a grain of salt :-).]
I'm not sure whether the initial dose affects the severity of the disease, but it seems clear that it at least affects the probability of infection. The individual action hypothesis [1] posits that each individual pathogen has an independent chance of infecting a host, i.e.
P(no infection | n pathogens) = P(no infection | single pathogen)^n
So if one is exposed to a single unit of the virus, infection is theoretically possible but unlikely. At higher doses infection becomes overwhelmingly likely.
I don't know how accurate the IAH model is, but there seems to be a good amount of evidence that infection rates are at least positively correlated with dose, e.g. [2].
[1] https://royalsocietypublishing.org/doi/full/10.1098/rspb.200...
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2869824/pdf/120...