Can I take admission in Jadavpur University and wait until the last round of JoSAA counselling for IIT?

Yes, but last year it was JoSAA which was completed first. After that WBJEE counselling occurred by which one can take admission into JU. JU is a very good university. Placement is also very good. But not like IIT. But one preference in JU is that it takes much less money from you than any IIT.