Yeah that’s fine, I took my last pill the night before the day I got my implant placed. You will not be protected right away but your implant will be active by the time you become unprotected from the pill, so there is no risk. If you have doubts then talk to your doctor or use condoms for the first week if it makes you feel better.
It’s uncertain if you will bleed or not as there is a chance the implant might stop that from happening but then again irregular bleeding is a normal side effect, which is more common during the adjustment phase of 3 to 6 months.