The Genii are in it for the Genii. The will be allies or enemies depending on where the percentage is for them. Given the right circumstances, they could slot into place like long-lost blood brothers. But if the balance shifts, Kolya will smile all indulgent-like as he watches John torture some poor Wraith and shoot him in the back while he's so pleasantly occupied.

The Genii may start by supporting the new Atlantis empire. But I don't think that would last once other allies become equally valued (i.e. empowered) and they realize they will always be second tier to the single-minded loyalty of Sheppard's core group. I see them as steadfast supporters right up until their attempted coup.

Oh, the possibilities!