Google's Paul Haahr, one of the most knowledge people around the Google ranking signals, said on Twitter that Google doesn't have a bandwidth ranking signal. He said Google did say they use both pagespeed and mobile friendliness as a factor but in terms of the bandwidth and connection of a device, nope.
He wrote, "Google has said mobile friendliness and site speed are important. I don't think we've said anything explicit about bandwidth."
Here is the set of tweets, so you have the context:
.@Photogkris Google has said mobile friendliness and site speed are important. I don't think we've said anything explicit about bandwidth.
— Paul Haahr (@haahr) April 25, 2016
Now, Google has done many things to try to speed up pages where users are trying to access it on poor connections. Including AMP and other methods.
We know Google will crawl more of your site if you return pages faster.
But the connection speed in terms of bars on a phone have little to do with the site itself and more to do with the searcher.
Forum discussion at Twitter.
Update from Paul:
.@rustybrick You’re making my statement more definite than I thought it was. https://t.co/K6IXUmRes2
— Paul Haahr (@haahr) April 25, 2016