Does "alpha" mean it is dangerous to use?

No. Not in the case of MakeHuman at least.

“Alpha”, “Beta” and “Release candidate” are just labels. In the case of MakeHuman:

• Alpha: there are unfinished features that we know we want to put in, or something we know we want to fix
• Beta: everything has been added to our knowledge, but we want to polish things a bit
• Release candidate: to our knowledge, everything is finished, but we want to test more

Traditionally, the alpha for the next upcoming makehuman release has been ‘‘more stable’’ than the last stable release.

At the point of writing this, MakeHuman is in the alpha stage for 1.2.0. Minus two points, MakeHuman Community alpha 3 is in most ways a better user experience than MakeHuman 1.1.1. The two things that are missing are:

• The FBX export has problem with rigs
• On some graphics cards, MakeHuman refuses to start

So, in summary: If MakeHuman 1.2.0 alpha 3 starts on your graphics card and you have no immediate need of FBX exports, then there’s no reason to stick to 1.1.1 for fear of instabilities. 1.2.0 is fully backwards compatible with 1.1.1.