You can "use" it with a 22 inch display. It should allow you to set the proper resolution and so forth. However, the 8600GT is quite an old card now and was only low to mid range when new.
At 1680x1050 resolution, you will probably be able to play modern games at low to medium graphics setting at best. If you are upgrading to a monitor this large and possibly can afford it, you really need to upgrade the graphics card and/or the power supply if you want to do gaming.
If you post more information about your system, such as CPU and power supply information we could give better advice.