Let's say you side with house and House prevails at securing hoover dam, and with the NCR and Legion are on their butt's rebuilding their armies...

Then a Ambassador for the Enclave, maybe someone like Arcade came to house with an offer of if They allow the Enclave to operate within the Mojave they would help house work on either beefing up his securitrons or creating a better Army.

You think house would take this offer or would decline the offer?

Take the offer because then house could control them and have them take Freeside being thought he hates the place so personally i think yes

I don't think so. The enclave would just end up being a third front for him to worry about. They can't be trusted. His securitrons are more than capable after they receive their upgrades.

No. A number of Enclave fans like him because his vision is similar to that of the Enclave. A restored America.

He wouldn't be in favor of their presence. Independence or Anarchy would be the best bet in that sense.

Oh and they could sort of have patrols all over the Mojave and the patrols could report back to him on the situation and get them to blow up the BoS bunker. Maybe...

What's the point? There's no Enclave in the west anymore. All you've got are a bunch of scattered survivors who are mostly, at this point, getting on in years. The fact that their organization has a dark history and bad reputation with the NCR certainly wouldn't help matters.

House would never simply submit to the Enclave unless he was forced to.

Whether or not he and the Enclave would be willing to do some sort of trade deal is a matter of debate. As what do the Enclave need (assuming they would be powerful enough to offer something to Mr. House) that Mr. House has? At the same time, I have doubts that Mr. House would necessarily want anything from the Enclave either. He's the man who's company helped to construct much of the Enclave's military might after all.

If a powerful Enclave met a powerful Mr. House (as a hypothetical situation) it would be a tense situation at best.

They share a similar vision, but that doesn't mean they will clasp hands and work together.

Ya true. Enclave vision of wiping out all mutants while House, well he probably does not care about them if they dont cause trouble. Despite though, I could somewhat see the Enclave working with House. House has research and technology from Big MT and maybe if the Enclave won and took control of Cali, then House would probably arrange a deal. We give you technology while you can pass are lands and protect us. This is my theory.