Time to get some sense into this thread. I wrote a short bit about berserks here (look further down in the comments to find searocks collection of relevant links), so let that serve as a tl;dr on the background.

Now, there are two ways to approach 'berserk studies': look at them like I did there, see them within an earlier pagan root of animal transformation (for which we have archaeological and pictoral evidence), which places them within a social tradition and basically makes them little more than a specialised group of regular warriors. By this interpretation, the 'berserk' would be pretty effective, as they are basically trained warriors.

The other approach is when you start from the Icelandic sagas, written after Christianisation. The berserks from the literature are a bit different, in that they are often just lone weirdos who go about Iceland making trouble and starting fights with random people. This is the kind of 'berserk-ness' that can be heriditary ('he is a berserk, and his father was too'), basically more of a way of life. Their role in the sagas often is that of a boogyman, a scary person, a half-monster. In that sense, they take over the literary trope of the half-man that Grendel has in the Beowulf, for example, who could also not be harmed by steel. These berserks have little to do with military fighting formations, and are mostly literary tropes (hence their later occurrence).

A real, historical berserk that an anglo-saxon in the 10th century might encounter in battle is thus a bit difficult to place. The most realistic form would probably be the first type of totemic warrior. In this case, their animal transformation training, or their membership of a bear cult, might help them in battle. Both the Irish annals and the Byzantine accounts of the customs of the Varangians say that these warriors would 'sing' and dance into battle. This is actually something that armies of the early modern period also did, as did the armies of antiquity (though not the Romans who were known for their stoic silence in battle). It increases morale. Coordinated dance (as is common in shamanistic cults) also is good training for group movement in battle, which is fundamental for the kind of formation shield/spear fighting that was common at the time. So yes, in that sense the berserk/bear warrior would probably be a very effective warrior, but paradoxically, because of their relative discipline.