I don't know if this is true, but it seems like the opposite would be more likely. In CTI you learn lots of terms and basic ATC concepts, but your not running radar simulation problems, memorizing realistic maps, newer things like URET and more. So it seems like CTI should have and advantage early, but later in OKC and in facilities when both groups are introduced to all new concepts, it should even out.
I don't know where you are getting your info that you don't run radar simulation at CTI schools, but that is not true. I can't speak for all, I can only speak for where I went, but for the terminal program at CCBC, we ran simulator problems all the time. There are actual classes called Approach I and Approach II, the airspace is Pittsburghs airspace, and we would run problems using that airspace. Some of the teachers are either current or former controllers at PIT, so they have plenty of experience knowing what the airspace is actually like, and the types of problems to give. The enroute program also spends most of their time in a radar lab running problems. Also, there is the best simulator of all for terminal, which is not a simulator at all, you get actual experience in the control tower that the school has the contract to run. I do have a CTO there.
Some may say that CTI is a waste of money, and just apply off the street. Well, I know some people that went to CCBC that are now working for Midwest, or Serco (I think that is how it is spelled) because they got sick of waiting for the FAA...how many people that are OTS can get a job working contract, none that I am aware of.
Both routes have their advantages and disadvantages, but you have to do what you think is best for you. I would be willing to bet that I am much more prepared than someone OTS once I get to my facility. I have worked traffic, I don't have mic fright (Is that how you spell fright lol?), I have dealt with other things that go with the job, like the interphones and stuff like that, so I would hope that I am much more prepared than someone OTS. Please don't interpret this as me being cocky, because that is not my intent, and I am aware that I am not guaranteed to succeed in the FAA, but I do feel like I do have an advatage once I get to my facility over an OTS person.