Do you think that using antithetic variables would be helpful in achieving the convergence faster in MCMC, that is, with less number of MCMC replications? Has an antithetic random variable implementation ever been considered?

Could be. Or the latter half of a single chain uses the antithetic numbers. But there could be some issues (not practical, but related to convergence properties of MCMC) with the second approach.

Unfortunately, I don’t. I do not have enough theoretical background to argue about the consequences of using AT numbers on MCMC asymptotic convergence either. However, I glimsped over some google search results, and I see some studies and notes regarding MC sampling and AT numbers.

One can run a long double chain MCMC with AT numbers to see if the variance is reduced, but this cannot prove the use of AT numbers. Sorry that I have not much knowledge in this topic.