Something>db9>db25>gender change, null modem or even a security dongle>back to db9> then a ps/2 connection> and the odd one out, a ps/2 to USB adapter for mice/keyboards> memory stick?
Probably not, if we're speaking about the next adapter in the line.
They both use 4 pins, and there are no active conversion in the adapter itself, it just connects the pins like this:
USB ↔ PS/2
+5V ↔ +5V
D- ↔ D
D+ ↔ CLK
GND ↔ GND
So, as long as next adapter is not doing something funny with PS/2 signals, it should be ok for bare USB 2.0 connection.