no, that is not the case for PS2 and serial mice... I have lots of these adapters , they don't work like that.
Sure , u can use a ps2 mouse on a serial port with them, but the mouse MUST support serial protocol, so it switches over (like the usb/ps2 adaptors)
on older 486/ealry pentiums, there is a seperate bios-like chip on the motherboard that adds ps2 mouse support. Even if the mobo has ps2 mouse header, without this chip , ps2 mice never work. (95% it is located left to the lower ISA slots) Some manufacturers even had a socket for that chip so the user can upgrade. Believe me, I have spent a silly amount of time on ps2 mice on older computers.
I am wondering IF with a simple re-wiring such adapter can work on a pc... if the serial and amiga protocols have the same signals (that I doubt)