You can, but you might be unhappy with performance and stability of your various GIS services. Typically, a good rule of thumb to follow is that a single core will support 4 concurrent SOC instances, which often implies a very small handful of very basic, simple services or one semi-complex service altogether. If you plan on having multiple services to be requested multiple times in a row by multiple users, then one core won't work. You'll see poor performance, and you'll likely experience timeouts and errors. Even for development purposes, I would recommend having at least 2 or 4 cores. A single-core machine probably won't cut it. There are plenty of good white papers out there for system architecture planning with respect to ArcGIS Server (at 9.x and 10.x), so I would recommend that you do some research. Another good resource is the Capacity Planning Tool (CPT) developed by Dave Peters at Esri. The only benefit that I can see to having a single-core machine is that your Esri licensing costs will be minimal. ArcGIS Server is licensed on a per-core basis. That being said, you get what you pay for.
