Can you create a circularly polarized signal with dipoles that are perpendicular but not crossed?
In theory you could, as in the far field both of these antennas will produce waves that seem to originate from approximately the same point. So from an observer in the far field, that is looking perpendicular to the surface of the antennas, these can product circular polarization. 

However, I think it will actually be harder to make, since in the case of crossed dipole, you gain from the fact that the fields of one antenna are zero along the symmetry axis. 
Here is an image to illustrate (simplified but should get the concept across). Vertical antenna has an illustration of it's fields shown. 



The nature of the crossed dipoles means that the differential mode (which is the mode dipoles work on) of both antennas is naturally isolated from the other. When you put them next to each other, this is not the case.