I think I understand what the OP is saying.
They're saying that if you start in D dorian, if you follow the CoF and go to A and play a Dorian mode, will you get the next diatonic key in the sequence. They just don't know they're actually asking this
froglips: you should learn the diatonic modes in relation to C major, the CoF and then translate what you've learned from the diatonic modes of C major into a new key. I'm assuming you can do both, hence your question in the first place.
So if you've learned that, you know the order of the diatonic modes from C major (ionian) goes like this:
C Ionian
D Dorian
E Phrygian
F Lydian
G Mixolydian
A Aeolian
B Locrian
It then stands to reason that if you move your ionian mode up a fifth, all the other modes must move up a fifth as well to be diatonically correct with the new key, which is G ionian.
So the sequence would then look like this:
G Ionian
A Dorian
B Phrygian
C Lydian
D Mixolydian
E Aeolian
F# Locrian
Make sense?