(Note: I am not an expert, just a student)
No, a type 1 superconductor does not necessarily have to be a single crystal. Being poly-crystalline means there are grain boundaries, which can count as defects in the lattice. To electrons, then, they look like scattering sites. However, according to BCS theory (accepted theory for type 1 superconductors), superconductivity occurs when electrons form Cooper pairs - they have a slight binding energy because as one electron distorts the crystal lattice, this slight distortion in the nuclei's positions is favorable to the next electron passing nearby. Because of this binding energy, it is much less likely that when 1 electron wants to scatter (like at a grain boundary), it will. Because this would require enough energy to break up the Cooper pair.
So no, a type 1 superconductor does not necessarily have to be a single crystal. Of course, it helps. I don't know how being poly-crystalline would affect the critical temperature, but my gut feeling says the Tc would slightly decrease for polycrystalline materials, if at all.