There will be an interference pattern, but not a visible interference pattern.
This is easily demonstrated: place a polarizing filter in the region where the two beams overlap, and a visible fringe pattern will appear downstream within that region.
If a polarization-sensitive recording material is placed in the region of overlap, a hologram will be recorded in the form of planes of equal birefringence -- instead of the usual form which is planes of equal refractive index or of equal absorption.