Honestly, I won't think so & I would think it would underpowered. But according to that site's Community-Based Activity section, it seams to support MythTV. So I guess if you can get a ARM version of Linux running & compile MythTV for ARM usage, I guess you could use it.
But at that cost, you can buy a Intel Atom330 mini-itx based mobo cheaper, which would give you more options & expansion options, for less cost. The Atom330 is a x86 dual core, hyper-threaded 1.6GHz Atom CPU (appears as having 4 - 1.6GHz CPUs within Windows). No problem with recording & playing back analog & ClearQAM recorded shows, using a Hauppauge HVR1600 PVR tuner card & the on-board video card. Also the power usage is very low (my whole PVR uses less then 30 watts).
But the choice is yours..
If you do happen to use a Beagle Board, please keep us posted as to how well it worked out & what it took to get working. I (& others I suspect) would be interested in seeing your results.