In general no, as was remarked in a sibling comment in this thread: SARS-Cov-2 on average spreads within the first 1-4 days after infection (viral titers peak on day 2 I believe), so the virus is indifferent to what happens after.

I also want to remark that there is the opposite effect that transmissibility correlates strongly with viral load (amount of viral particles) and viral load correlates weakly with lethality.