Sonic you have the wrong diagram for the manual climate control instead of EATC.
On the EATC circuit, one transistor for the speed control is what some erroneously call the blower motor resistor (module), mounted on the firewall. A second likely transistor is located in the EATC head unit to bias that speed control resistor, with that head unit on a EATC replacing what is on the manual diagram as "Function Selector Switch Assembly".
My thinking is that even if the blower motor relay is stuck on, the EATC module itself should still be in control of if it turns at all. In other words the relay has to be on for the fan to run in the lowest mode possible, so the EATC has to be in control of the fan still (or not in a failure condition).
I state this with the assumption it is running faster than the slowest possible speed since the OP reports it is noisy. The other option for particularly noisy might be a shot motor bearing so it is louder than it would otherwise be, in conjunction with another fault.