Anode rod debris on bottom of tank
It is detrimental the same way as sediments that will work their way through the pipes and create blockages in shut-off values and clog up the aerators filters in the faucets.  You just replaced the rod,  Continue with a deep flush of the tank and remove the sediments from the bottom of the tank.  There are YouTube video on how to do a deep flush but it consists of:
1. Put hot water on pilot or vacation mode
2. Shut of the water at the top of the heater
3. Drain the tank
4. Open water valve at the top of tank with drain faucet still open.
5. Run for about 5 minutes or until water is clear and no sediments is flowing out
6. Close drain faucet
7. After tank fills, turn gas back to your normal setting

On "Corrosion standpoint?"  If any magnesium  or aluminum broke off, it will continue to perform its duty of rusting first, same as if it was still on the rod.