No. The vaccine will stop the replication of the virus in your system. You won't have enough to spread. Your body basically kills the sob before it replicates enough to make you and others sick.Wow. Stooping pretty low there.
But let me pose this question...and I don't know the answer but I suspect that since an asymptomatic person can still spread it I am assuming a person who has gotten the vaccine can still spread it? If that is the case then it doesn't make any difference to you if your next door neighbor got the vaccine or not?