Is your cable an RS232-to-USB, or is it a USB with something like TTL inputs?
If I were designing this, especially if a high sample rate it required, I would use an RS-232 to USB (or SPI-to-USB or I2C-to-USB) cable along with a microcontroller. The microcontroller would monitor the input and accumulate rising edge or falling edge counts in an interrupt routine, and then send that sum, upon request, to the PC via the USB connection.
I might even consider using a "USB enabled" microcontroller, and by-pass the serial-to-serial converter (i.e. connect directly to USB).
But, if that's outside your experience domain, then what you are proposing should work, as long as the sample rate doesn't need to be too high -- but, no, I don't know what that threshold is. Perhaps you could contact the RobotBASIC people (or maybe they have a forum).
I also don't know if RobotBASIC can service interrupts from the USB port (probably more like an "Event"), but, if so, that would be the way to go.