Replacing a tube HV rectifier tube with a solid state one

[Electronic M]

They should not effect the flyback if disconnected. That assumes you mean disconnected from the rectifier socket. If they are still wired to the socket there one effect they could have: if one end of the winding is connected to HV (as is usually the case) and the wire insulation has broken down at a point it touches the chassis or is wrapped around the flyback the breakdown leakage can kill the HV level, load down the fly and even damage the rect.