I have tried it both ways. I have not been able to tell that a crimp helps at all; so I do not mess with it. I have 3 different guns that shoot 22 Hornets and they are all single shots, so no worries about bullet set back for me. I have found that if I get enough grip so that I can not move the bullet by gripping it with my fingers and pulling, I have enough neck tension. I have neck turned 223 cases down to the thickness of a 22 Hornet case and I do not have any problems; I get very good accuracy and I do not crimp those either.
BTW I now use pistol primers in my 22 Hornets. It takes more powder and I get higher velocities and longer case life. Read about it in Speer manual #14.
When ever you crimp ANY cartridge, it must be done very uniformly. If not done uniformly it will effect velocity from shot to shot. It depends on the crimp being done - but if you are using a die that crimps as it seats, the cases have to be the exact same length so that each crimp is the same and you want to do it in a groove that was put in the bullet for this purpose. If you try to do this with out a crimping groove, you risk buckling the case in the neck area. This limits seating depth and type of bullet being used. When using a Lee factory crimp die, case length is not as critical and it will crimp into a bullet with out a groove, but setting the die so that each crimp is exactly the same is critical. It is much easier to not crimp. With the 22 Hornet, I just make sure there is a generous chamfer in the inside to aid getting the bullet started with flat bottom bullets. I have a set of RCBS dies that will crimp if set properly for it and a Lee set that will not crimp, no matter the setting. That is what they sell their factory crimp die for.
Good Luck and Good Shooting