That depends and is a curiously tricky question to answer. For example I RP a thourughly puritanical member of the Enclave and the thought of House colonising another planet with mainlanders drives him mad; consider this the Enclave's 'Brotherhood of Steel Zealots who kill the Followers'.
As for the Enclave as a whole on a more tactical desicion, as of 2281 he presents niether a threat nor anything of interest; the Enclave will be fully aware on hiberation technology and aside from that House's promises of a better future for the human race aren't as narrow minded as the Enclave's and nor are they in any position to be acted upon without someone like the Courier to save him. I would put it down to House actually whom I can only imagine would give the Enclave the same treatment as the NCR, House is typically indifferent of these organisatoins and would probably tolerate the Legion if they didn't threaten him. It would also depend on who was in charge, Richardson for example in Fallout 2 has respect for the Vault 13 Dwellers and commends them - sincerly - for their sacrifice in helping save their - as in the Dwellers and the Enclave's - nation; I can imagine that Richardson might afford House some degree of liniancy unless House proves a threat. But seeing as how House wants to resurrect Vegas and the Human Race whereas the Enclave is largely concerned with the survival of the human race but on a more extremist scale - i.e. simply start again. House would have survived Richardson's Porject but then if the Enclave contacted him what would he do? He would have no Vegas to be able to build and literally nothign to live for.
Well the virus would have destroyed the current population of las vegas (would never become new vegas).
Assuming Richardson had succeeded, and begun the 'restart' who would make a greater ally than one of the most brilliant minds of the pre-war era?
In the game new vegas represent nothing more than a source of income to house, a means to build an economy that would drive his second industrial revolution.
I'm assuming the Enclaves aims would be synergistic with House? He wouldn't neccessarily need the funds of vegas if he was allowed to use Enclave resources.
There is one glaringly obvious problem with this though, I'm not too sure House would submit to command of the Enclave and vice versa.
Even if they worked in unison on the rebuilding effort, there would eventually be a power struggle of some kind.