Yes and no. Angelfish are shoaling fish, meaning that they naturally live in smallish groups. They develop a social hierarchy within the group. A sole fish will thus be deprived of what nature intended, but too many aquarists have maintained healthy sole angelfish to say it is not possible. The worse case is having 2, 3 or even 4 angelfish (except for a mated pair which is a very different thing), as in these cases there is every liklihood that one of the fish will bully one or more of the others.
The other community fish are very important too. Active fish can unsettle the sedate angelfish. Obviously, community fish must not be any of the species likely to nip fins. And they must be large enough not to be considered food by the angelfish. A mature angelfish can easily eat a mature neon tetra for example; I've seen it, and my angelfish was no where near full size either.
This seems a good opportunity to post a video I came across some time back, showing a group (around 11, I believe) of wild-caught angelfish in a very ideal captive environment. You will observe the very sedate behaviour of these fish; they do not swim around much, they remain together and quiet. Their hierarchy is plainly evident, as practically each fish takes a little "poke" at a more passive fish within the group, but never leading to any physical contact. This is how they behave in the wild, and how they behave in a realistic aquarium habitat. The only other fish are corydoras which are not going to pose any issues for the angels or vice-versa. This is truly observing a bit of nature in an aquarium.
Byron.
https://www.youtube.com/watch?v=9gXVgWLbZ-g