Apparently not. I've had many people comment on other websites where I posted this article that say these logos mean nothing to them when posted without a header or confusing lines like that.
What I wanted to point out is that this form of social proof is being used everywhere - so it's more important than ever to present it properly for it to be truly effective. I've heard some SaaS consultants say startups place logos on their website even if one person signed up for a free trial (and never ended up becoming customers) or signed up to their mailing list. That's deceptive marketing and I think it should either be done properly or not done at all.