Can boundary layer theory be applied in finite element methods as it is applied in finite volume method? i.e The flow away from the boundary is considered inviscid and solved first, then the flow inside the boundary layer is solved?
It can but you are wasting the full potential of the method when doing it so. I recommend you look into "Applied partial differential equations" by Trim. You can also check a few articles in perturbation theory which solves part of the boundary layer. Doing finite element is just useful when you are programming it.