Yes, beagles do indeed play fetch. Beagles are just like any other dog. What they can and cannot do all depends on how much time you decide to put into them. For proof that a beagle can fetch, you can watch my dog, Nova, playing fetch in the video below.
My other beagle, Cosmo, was not in the mood to play fetch at this time. However he is actually the better fetcher.
That is one thing that you have to know about beagles. Just because they know how to do something, does not mean they will. You have to catch them in a playful mood.
In order to teach beagles to play fetch, you have to be patient with them, and put in the time. It is hard to hold beagles attention for long. This trait makes them quite difficult to train. Be patients with them. Remove any distractions, and start simple. Before long, they will be fetching in no time.