Yes, there are references to God as rock, and certainly to Christ as a variety of architectural objects, including Christ as foundation of our faith, but here we have two candidates, Church and God, and of the two it is the Church that more readily invites the architectural metaphore.
No, of course the other reading does nothing to Catholic eccleseology either.
I wouldn't say that the church more readily lends itself to an architectural metaphor - especially when you see God Himself used as an architectural metaphor throughout Scripture. When Christ returns he will not come for a building, he will come for a people. So, with either God or the church you are dealing with living organisms (for lack of a better word). The metaphor could apply to either appropriately. Again, I think it probably is the church but I can't be adamant about it - nor can you all. God Himself is the truth. So it makes sense that He would be the supporter (pillar) and ground (could be seen as foundation which we know the chief cornerstone thereof is Christ) of the truth just as He is the life and the giver of life and the Lord of life etc.,
Not something any of us can absolutely hang our hats on from a Scriptural point of view. Now, if you claim the authority of the church for its interpretation ,that's a different thing. But we were talking the actual Greek Grammar here. And it isn't conclusive.