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That maybe the case of going forward into the future,but i cannot imagine one million or even a trillion time travellers doing that at once,the irony is the afore mentioned April1st.
But travelling into the past is another,entirely different action indeed. The laws of temporal causality dictates that if you go back in time,just being there alters the whole space,time continuim stream and you end up in a whole new time line,so you could not go back to your original present if you wanted to.......................scary eh!
An infinite number of timelines could indeed cross and you might end up back at your place of origin........................probably after a billion tries;but the universe is a wondrous thing and there are so many things we have yet to learn.