If I use modifier in the modeling phase, do I have to apply the modifiers (particularly the mirror) before I can work with...

The UV's are only editable on the original mesh, but in using the mirror modifier, whatever UV/texture is on your original mesh will be mirrored to the other side. So you can use that approach efficiently. But if you don't want your textures mirrored then you will have to apply your modifiers before UVing.