First thing, is of cause he can be re-inserted, how do you think humans got into the matrix in the first place? They did start by inserting adults. Second is that machine have never been show lying, they only think logical they either do it or they don’t, and the sentinels where just a continuants plan for the machines, they where expecting to get the codes not destroy everyone one the ship including mophues (and the codes in his head)
regards, godfather