As far as I'm aware, almost certainly not. There is no such index dedicated especially and specifically to whether any two (or more) characters from the mythology interact with each other (or with one another) or not.
I would say that the best one could do in approaching something approximate to this would be an encyclopaedia, in the use of which sometimes it's easier and other times more laborious to search out whether two characters ever interact in the mythology or not.
Particularly in order to answer certain StackExchange Mythology Questions I have to had to employ the use of such a resource, generally going by a combination of:
There's an "Enhanced by Google" Search function one can use inside the GML and Theoi websites to perform a scan limited to only those sites while inside them. It's definitely not as sophisticated as calling up a couple of names and finding a Yes or No response regarding their possible interaction. Sometimes you'd have to skim through a few dozen Search Results to determine the answer to your query.
Often enough the interaction in question might be something along the lines of "These two gods had altars next to each other in the agora of that other city over there," and that's it.
If one of the characters in question is significant enough, s\he will often have her/his own dedicated Page on Wikipedia, on the GML or on Theoi. I often default to Theoi, where I would then simply perform a Find-in-Page Search of that particular webpage to look for occurrences of the other personage's name regarding whom I'm wondering whether s\he interacted with the first personage in view here.
The chances are that if you don't find the interaction on Theoi then it doesn't occur in ancient sources, whether literary or artistic. There is, however, a lot of material in the corpus of what we refer to as Greco-Roman mythology, and I doubt that any one of the aforementioned resources, in isolation, suffices to cover absolutely every possible source, some of which can be pretty obscure.
