Your statement doesn't even make sense.
1) search engines are not users, so it can't be 'user friendly' to a search engine.
2) search engines don't have EYES, so they won't EVER see your responsive design, or really ANY design in the first place. ANYONE telling you that "design" has ANYTHING to do with search doesn't know enough about the web to be opening their trap on the subject!
So saying that the two interact is just gibberish. Completely unrelated.
Now, part of building a proper accessible design CAN impact search, and that's commonly called "semantic markup" or as I'm starting to call it now, "USING HTML PROPERLY". If you start out with your content or a reasonable facsimile of future content, mark it up semantically -- you have the content and markup saying what things ARE -- and search engines WILL use that, and to be honest that should be the be-all end-all of what on a website would impact what a search uses.
BUT - BAD design CAN impact your rankings, though that has nothing to do with the layout; it's because Google and other engines are now penalizing poorly written bloated slow loading presentational image heavy sites... the laugh being the 'bad' part of such designs is often the very pretty but ultimately useless garbage the ignorant fools who draw pretty pictures in Photoshop then have the giant set of brass to call themselves "Designers" come up with, often mated to the flashy but ultimately useless JS that scripttards piss all over sites with using bloated nonsense like jQuery.
But that has nothing to do with layout.
Really you want to see what a search engine "Sees" on a website, disable CSS and all 'style'. Lemme use one of my sites as an example:
Older site, not updated in a couple years... but it's a elastic, semi-fluid and responsive design... and none of that has anything to do with what a search engine would 'see' -- because again, search engines don't have eyeballs. The closest you can get to what a search engine would see on that site is to disable all styles; keeping in mind it also uses semantic markup so it would ALSO see that.
Here's a screencap of that:
Search engines see tags for what they MEAN, which is why mis-using a tag (like tables for layout, P as a heading or P around a IMG) is as bad or even worse than using no tags at all. Other than that, they see your plaintext, NOT your fancy visual layout. Fancy visual layouts are for sighted users, AND THAT'S IT. People using screen readers don't see it, people using braille readers don't see it, and search engines not being 'sighted' either, don't see it!
Anyone telling you otherwise is blowing so much smoke up your backside you could enter your ribs in a BBQ competition and probably win.