No.

Everyone – vaccinated or not – will need to continue all current recommendations regarding social distancing, wearing a mask, and avoiding travel. This is because up to 10% of vaccinated individuals will not be protected from getting COVID-19, and because reinfection, while uncommon, can still occur. And the vaccine itself doesn’t prevent you from contracting the virus; it simply prepares your body to mount a vigorous defense so that if you do become infected, the resulting illness is far less likely to be life-threatening.
– excerpted from AARP Bulletin, January/February 2021, Vol 62. No. 1.