While PS/2 keyboard to AT keyboard seems fairly straightforward, I'm not so sure about PS/2 mouse to 9-pin serial mouse. It appared each manufacturer had their own adapter, and probably different drivers too. If the combo controller has its own driver, I believe it could be difficult to connect it via a serial port adapter.
A bit related is that I tried to connect a Microsoft PS/2 mouse to the serial port on my old Pentium (I know, not vintage enough, but I gather it would work the same way on a 386). I used the adapter that came with the mouse, and installed a suitable driver. It works fine as long as the mouse is attached directly to the serial port. Then I added a KVM switch inbetween, and the mouse is no longer recognized at all! Absolutely dead. The Pentium also has a true PS/2 header on the motherboard, which I assume is for mice. I installed the suitable cable and connector, but it would not work with any mice at all. In the end I solved this by having two mice at my desk, the Microsoft PS/2 one for my major PC and an old serial noname one for the older computer.