From previous work, I would suggest that you shouldn't be able to notice any difference between the "empty" cultures and those containing the uninduced plasmid (should also be very close when induced provided that you are not expressing a toxic protein). As for the growth rate, "Timing the start of division in E. coli: a single-cell study" published in 2008, Reshes et al. suggest roughly 38 minutes for replication in M9.