Yes. Omron supply and support CS1W-CIF31 product for connecting to the serial port of an Omron PLC from a PC with only USB ports and no RS232 serial ports.
There are a large variety of third party USB port converters on the market and we haven't carried out a structured testing program with them. Every USB port converter emulates a serial COM port but the emulation may not be 100% compatible. CX-Programmer will work with any USB port converter that it is 100% compatible, although the only known device is our CS1W-CIF31.
Note that Windows 2000 has poor native support for USB, but the latest Service Packs and Windows Updates usually resolve this.