Yes, a house that has been clad in brick can be relocated. The bricks are removed (demolished so not reusable) prior to the shift and once re-sited the house can be re-clad in any material. It also allows easy access for re-wiring, insulation and adding in extra power points.
We love relocating brick clad houses, as it gives the re-locator a completely blank canvas to renovate the house into something they love.