The answer to the simple question -Is 2MP high enough quality to print a 4x6? - Is yes.
Especially if these are just being used for "fun" display purposes and not in a professional manner. They also would be suitable for most online use.
Diving deeper in to the details of your question though, you are asking if your point and shoot camera is a good solution to take 4x6 printed photos of sports. 4x6 photos are not the problem, but you might run into issues with maximum shutter speeds not being high enough, causing blur in the images, or on the other end of the spectrum even a blown out image.
The big advantage of a DSLR or higher end camera, would be the ability to shoot at high frames per second, for longer periods, at a higher resolution. They also will do a much better job at focusing in on your subject, and be able to do all of this at a moments notice even when the camera is in standby mode. A compact or point-and-shoot camera likely will require you to prepare for the shot by keeping the camera on, and even pre-focusing before the "moment" to get the shot you desire. Otherwise you might end up with 10 frames that capture the moment right after all of the excitement.
In my opinion, I wouldn't rush out to go get a new camera or SLR. I would be comfortable taking shots with an iPhone 4 of an event like this, with the goal of printing a few 4x6 photos for other employees to view online or on a community board. Professional equipment is not a necessity, it just will allow you to do this in a more varied environment, to get crisper high resolution shots that can be printed larger or cropped more.
Update: The other answers here are correct in pointing you to PPI and
DPI - but in my opinion, for non professional 4x6 use, just about any
camera under the sun including most current cell phone cameras will
produce just fine prints. I know people(my wife) who strip 72dpi
Facebook images directly off the web and print them. They are
perfectly acceptable to non-photographers who are expecting
This is all assuming the sports are played outdoors, or in very good indoor lighting. If the lighting is poor - you are going to have trouble with anything but professional equipment to do sports.