Does the covid-19 vaccine cause b cell and t cell memory? will a t-detect test show a positive response?

Nearly always the immune system has a memory the degree and length of which depends on many variables. Pl do not worry about hypothetical scenarios and tests. Tests like these are expensive and should only be done if indicated and ordered by an MD

If you have been fully vaccinated a few months ago, there is absolutely no reason to waste time or money on so-called antibody testing, as true immune bodily function is far more complex, and the anticipated responses of the innate and adaptive immune systems are best illustrated when infection contact occurs.