Will a standard RS-232 DB25 to DB9 adapter or cable work with my RS-422, RS-485 board?

No. Standard DB25 to DB9 adapters and cables are made to convert an RS-232 DB25 pin out to an RS-232 DB9 pin out. As such, they do not pass the correct signals through for RS-422 or RS-485. Please see the following question regarding using standard RS-530 cables or visit the cable accessories page for cabling options.