Can objects be extruded during game play in Blender's game engine? If so, how would I do this?
Depends on what you mean with "extrude".
In terms of mesh-editing the answer is no. This is simply because you can't add faces to meshes from within the BGE.
As this does not help you with what you want, I suggest to get rid of the "extrude face" idea towards an "extrude effect". It does not add faces, but deforms the mesh in a way that it looks as it would do that.
There are several ways to achieve that:
- armature deformation -> it can animate scaling too
- shape key deformation
- scaling animation -> would effect the complete mesh
- mesh manipulating via Python (not a simple task)
- adding objects ...
Without more information I can't tell what option is sufficient with your situation.