I have not taken a rimless case and test fired it, then cut a rim in and test fired again to see if you gain anything. I would suspect you would gain nothing as far as accuracy is concerned. My understanding is, if a case has a rim, you get best accuracy if you head space off of the shoulder, not the rim. Some cases such as the 22 Hornet and to a certain extent the 30-30 do not do a very good job of head spacing off the shoulder because the shoulder is too sloped to do so. Many early cases were head spaced off of the rim and had very sloped shoulders or no shoulders at all. A modern rimless design forces you to head space off of the shoulder and thus, in general, has better accuracy than a rimmed design. With all of that said, I still prefer a rimmed case in a break open single shot. Why might you ask? No real solid reason, I just think break open rifle and rimmed in the same vein.
Rimmed vs rimless has been debated here many times and some people have strong feelings both ways. My personal feeling is do what you like, feel comfortable with. I have seen rimless designs shoot well and I have seen rimmed cases shoot well. So once again, it is a matter of preference. I have 6 different barrels and only 1 is rimless, a .223 Remington 24" Bull. It is not my most accurate barrel, but not because it is rimless.
Good Luck and Good Shooting