How would you feel if they integrated Portals into a Half Life game? I know their have been some vague rumors about it, but I'm assuming their just rumors.

 Still, if they did it properly (which I don't doubt Valve could easily do), I think it could end up being a pretty amazing game. Still, it could slow down the action or make parts of the game too easy; again, it would have to be added in very ingeniously.

Do you think this could work in any way? Or do you think it would lessen the appeal of both the Portal and Half Life elements? 

Well, Valve has started to link the story of Aperture Science in with Half-Life from what's happening near the end of Episode 2. In fact, we find out that the tanker you're going to be looking for suddenly disappeared so it could mean that it has some sort of portal technology on that.

While not official, somebody has tweaked the game to add the portal gun in Half-Life 2 (I think the video was showing it in Episode 1). However, the AI really had no idea what was going on, but it was cool when the guy used portals to get around.

This is no alien idea for those who played the original Half-Life back in 98, there were in fact portals in a few levels, brought forth by tears in time and space at the very beginning.
Also, this is a likely scenario seeing as Newell of Valve software has said numerous times now that Portal gameplay, or at least segments of it, could be a major part of Episode 3 due late this year.
I'd not oppose myself to a fresh breath in what might possibly be the stalest game genre of them all, but regardless of such fancy plot and gameplay turns, I remain confident that one of PC gaming's finest dev's will continue making smashing games!
Can't wait for Episode 3 and that alledged Half-Life 3 teaser supposedly following in its wake on Steam!

The most recent quote from Gabe that I've heard was basically this:

"The developers have full access to that feature and there is no work involved in adding it since its already in the engine. If they feel like it fits or they have a place for it they will add it in..if not then they won't. We've learned that these gameplay mechanics are fun but that its best not to forcefully work them in but rather let it flow naturally. Trying to force it often shows through in the final product and we've had some amazing results from just letting things take their natural course...so thats what we've decided to try doing from now on."

-my paraphrasing from a GameTrailer's interview