Yes, that looks suitable.
The pin connections you listed are for the connector on the back of the PC, which has male pins. The Pololu board has a female connector and appears suitable for connecting to such a PC serial port, either directly or with a 1-to-1 wired serial extension cable with a male at one end and female at the other. In that case, this adapter will have pins 2&3 swapped from your pinout in the OP, (Billy's Law notwithstanding).