Not in your case, where you have a separate coax line from your central panel to the router location enabling an alternate path for the MoCA signals.
However, absent this extra coax run to the router location *and* no Ethernet connectivity beyond the devices co-located with the router, the MoCA signal would have needed to travel on the modem’s coax line, which would be especially problematic if the modem line were an entirely separate run from the provider — putting aside the unique difficulties that would have been posed by the current amp location.