Way of White Coop: any decrease to invasion chance?

Read on the wiki that if you're in the Way of White, decreased chance of being invaded. But it also says it seems to removed this if you summon another phantom. It doesn't say if the phantom you summoned belongs to any covenant.

So my question is:
If I'm in the way of white, and I summon another way of white phantom, do we still have a decreased chance of being invaded?

Cheers