connect my rs422 to my computer
Yes, loopback should work. B&B makes good equipment and has for many years. If you converters are powered from the RS232 line, then you cannot just unplug them and jumper transmit to receive as the unplugged converter will not have power. You can contact B&B support for details on looping back your particular converters.
Here are some other ideas of how to troubleshoot. Get two computers some cable and two of the RS232-422 converters. ( One or both computers can be laptops, and old ones work fine for this.) Connect the converters to the computers and then attach the cable as normal. On both computers, open a serial port terminal program. Windows ships with one called Hyperterminal. There are many others, some are free. TerraTerm also works well. Configure the serial port terminal program for your baud rate and whatever serial port you attached to. Turn off any hardware handshaking. Also turn off any local echo of characters. Tell both terminal programs to "connect", in Hyperterminal, I think you have to click a button that looks like a telephone. Now start typing on one computer, if the cable and converters are good, then the output should appear on the other computer. If you go to the second computer, you should be able to type messages back to the first.
Lets call the computers "A" and B". Take them to the customer site and connect "A" at the PLC end and connect "B" at the first display. Again open the serial port terminal software, configure as before and type on both keyboards. If "A" can type characters to "B"'s screen, but "B" cannot type to "A", then the return path is broken. If "B" can type characters to "A"'s screen, but "A" cannot type to "B", then the transmit path is broken. If neither can type to either, then you got a shorted or cut cable.
If either computer shows characters but they are wrong or jumbled, the cable is got a broken wire or an incorrect splice. These are twisted pairs, if the cable is connected wrong and one of the transmit wires is twisted with a receive wire rather than its mate, then really wierd stuff happens.
Once you have the two computers talking over the customer's cable. Reattach the PLC in place of computer "A". And monitor the screen of computer "B" when running the PLC. You should see the traffic on the cable. If it is binary data, it will appear as a bunch of nonsense characters. This is OK. The big thing is something came through.