Actually, the old stems/vines pull off rather easily :-) My own SAC, going on some 20 years old, rapidly outgrows its metal trellising support very early in the season and invades an old apple tree, a large nearby butterfly bush, a burning bush and everything else in its path. Cutting back each season involves pulling the old vines out of a variety of trees and shrubs and I've not found their removal to be a problem. Certainly not to the extent of pulling branches off trees.

My only concern about your proposal is that once the vine becomes well established, its top growth may shade out the fir too much and affect its growth or foliage. This may be something you will need to monitor going foward.