From what I've heard, a true grafted coral wouldn't need both colors to be present in order to grow and develop them- that's why (assuming the purple was a third grafted coral and not just a natural development of the red or green Monti) that purple would be able to develop even when there was little to no purple on the original frag. That assumption is a bit shaky because the frag likely wasn't showing
Here's an example of what I'd call a fully grafted coral: (From WWC)
I believe if you were to split this frag anywhere, it would continue to grow with both colors , since the pigment was actually exchanged between the two corals. Notice how there's spots of red that are entirely surrounded by green and vice versa, meaning that there had to be the ability to produce both pigments.
Whereas of you look at this, it appears that there is very little exchanging of pigment, meaning that this one may not be fully grafted yet (It very well could be and just have a growth pattern that's different from the one above, but just for the sake of example, assume this one was freshly grafted, meaning the two corals were cut and placed together and now grew together).
In this case, I would guess that if you took a piece off of the far right, it would grow into a fully red colony. If you took a piece off of the far left, it would result in an all green colony. In this case, although it grew together, I would say it's not truly grafted because the only section that has exchanged pigment (if at all) is at that intersection. That's very different from that first frag, where even if you broke off an all green section, chances are there will still be some red mixed in there. Now if you took a piece of that intersection, those two corals could either just grow together and form a hard line without exchanging pigment, or they could graft.
Long explanation short- To answer your question, if a coral needs both colors to be present to maintain those 2 colors, I don't believe they are truly grafted together.
But I'm a non-expert on this so my opinion is just as good as any other hobbyist- don't take this as fact until we can get a true expert's confirmation lol.