So basically, I have a mesh that is moving via a constraint. However, because it is a constraint movement, I can't find the position of the mesh. So, is there any way I can find the current position of a mesh, even when affected by a constraint? (I mean like in numerical form)
Presuming you can see the model in object mode, Select it and press SH-S, choose "Cursor to selected". The 3D cursor will jump to the model's origin point. Press N and you can read off the 3D cursor's location.
If you want to store this within the Blender file, ADD an Empty. It will appear at that location and it's own location readings at right will be the same as the 3D cursor's.
You haven't stated what constraint(s) you're inquiring about so I've just tested this out both with a path constraint and parenting the object object to another. Both work as described.
Every object has a matrix world, that is the resultant global location, rotation and scale, after keyframes and constraints etc are applied.
To see the current global location, with the object active, go to the python console and type in
>>> C.object.matrix_world.translation Vector((0.0, 0.0, 0.0)) >>>
to see its visual global location. Might seem a fair bit to do but once you have typed this in once to repeat press up arrow (history) , return.