Ha while I can't say I've invented any crossovers myself, I think you're going a little too far with the theory. Even though GladOS's song suggests that it's alive, I think the sense of humor of portal probably won't carry on into HL. I believe the first part, but the use of the portal gun in ep3 doesn't sound right to me, mostly because I think I've heard it as a confirmed no. Still, I doubt we'll fight gladOS, I think they'll just drop her in as a fun easter egg.

Just what I think.