Probably not. I doubt they will test you for antibodies. That would say if your vaccine worked.
You might get an antigen test to see if you have an active infection. But probably not if you have no symptoms.

I would just quarantine so you can't infect anybody else. Everybody you live with should quarantine as well. The normal course of Covid-19 is:

Day 0: Exposure.
Day 3: Virus level gets high enough to be detected by PCR.
Day 4: Virus level gets high enough to be detected by antigen testing. You become contagious.
Day 5: Symptoms may develop.
Day 9: Virus level drops so you are no longer contagious. Antigen tests go negative.
Day 15 (or longer): PCR tests go negative, because they show positive for dead virus fragments.

So you can see from the timeline, quarantine is indicated from 3 days after exposure until 9 days after exposure.
Of course, some cases can take longer to progress.

We're flying electric helicopters on Mars yet you can't turn on your clothes dryer in Texas. That's because scientists are in charge of Mars, and Republicans are in charge of Texas.