For me the thing that took the most time was the porting of the number over from Verizon to Visible. I do not think e-SIM versus physical SIM would have mattered much. If you are not keeping numbers then yes, E-SIM could be same day service.
I do not think you can have multiple phones on one account on visible, so each phone would have to have its own account on visible. Which I believe means unique email address. You can use the same method of payment on all accounts, but there would be a transaction for each account.