The big question is where you stand on ascribiong the system of late Roman government to Diocletian. If you are willing to credit him with inventing the post-Tetrarchic state, then it is unlikely that the Empire will survive. If you are unwilling to take that view, then removing Diocletian will have few immediate effects.
First of all, Constantius Chlorus was a capable warleader and canny politician, so it's likely he would have made as good an emperor as Diocletian. Given that organising the succession and heading off challenges from military commanders was probably the major problem of the age, he would have had to find a solution to it or perish. The tetrarchy wasn't really the solution - multiple emperorship was - so any system that allowed that would do.
The msin question I hae would be what Constantius would do about the imperial administration. THe system, we can discern in the fourth century came from somewhere, and if we go on the assmption that it is a tetrarchic product, he would have to come up with his own. Without it, I suspect the Empire is doomed.
Religiously, the rule of Constantius is unlikely to benefit Christianity. The laws will probably stay on the books and local persecutions continue, and by the time the first anti-Christian emperor joins the government (however this is organised) we will still see oprganised persecution. Diocletian's tetrarchy eventuially brought forth the Edict of Salona, and I doubt we would see anything like it in a more disinterested system. Of course, if Constantine still converts, we could see interesting developments down the road. I doubt it will go as smoothly as OTL, though.