Okay, so here's the thing. I've been looking for a build that I can pull off that doesn't violate any rules or needs outside support books to do. The build; up to level 20; is this:
1 level Fighter
3 levels Wizard
3 levels Cleric
2 levels Mystic Theuge
10 levels Eldritch Knight
1 level Mystic Theuge
It pans out; at least in my mind; into the char being able to cast as a level 15 Wizard and Cleric, with the ability to take feats that require you to be a level 11 Fighter to take.
I justify it by combining EldK. with Mystic. For the EldK. from level 2 through 10 you gain spells as if you had gained in your arcane spell caster class. Mystic, due to it's abilities, is technically an arcane and divine spell casting class. So when I gain my levels in EldK. I choose Mystic as the class I want to gain my new spell casting abilities from. Because Mystic's spell casting abilities raise both divine and arcane at the same time I gain both. So now I've just gained; at level 10; 9 levels of both Wizard and Cleric casting abilities. So now I cast as a level 14 Wizard and Cleric. Finish the 20 level build with an additional level of Mystic Theuge to maximize my spell casting abilities.
I'm pretty sure there is no RAW on this subject because the devs didn't think anyone would try this.
If you brought this character to my table I'd say that Mystic Theurge does not grant you any spellcasting ability, it only advances the spellcasting abilities of classes you had before entering the PrC. Therefore, it is NOT an arcane spellcasting class and cannot be advanced by Eldritch Knight.
Your GM might rule otherwise, but this smells an awful lot like provolone to me.
Nope, doesn't work.
You even said it yourself... you do not cast "as a level X mystic theurge" you cast as a level X wizard and a level X cleric. You could take Eldritch knight to continue advancing Wizard casting, but it would not advance both.
All of these PrCs advance your spellcasting 'as if you had gained a level in a class that grants spells'... which points out right away that the PrC is not a class that grants spells in and of itself, which makes sense... there is no Mystic Theurge spell list, for example. Even the simpler Arcane Trickster or Arcane Archer PrCs are not arcane spellcasting classes for the purposes of these sorts of abilities... they just advance an arcane spellcasting class that you already have.
No. Eldritch Knight cannot be used to advance Mystic Theurge.