this usually works well with business partners. I've worked for a company that manufactured industrial electronic devices (PIDs, themrographs, humidity probes, etc) in 2014 and our site had about 10-12 logos of other companies (usually companies that we were doing business with by either buying materials from them, or selling to them) on our site...
And back then I was being in charge of this company's Adwords campaign and I - inevitably - had access to their analytics, too, and I could see that some of the traffic that we got (via Adwords mostly, but also via SEO) was clicking on these logos (that were displayed in the bottom of our homepage, right above the footer).
So, some of this traffic (I think about 3 or 4% but I don't remember, it might have been higher, but under 10% for sure) were clicking on those logos so I assume that - eventually - some of these clickers have ended up becoming paid customers for our partners. I mean, they had to, you can't get so much relevant traffic week in and out and not make any sales, that'd be disappointing...
As for our site, 1-2% of our traffic did come from our partners, probably in a similar way (by clicking on our logo on our partners' websites), but I don't remember whether this traffic had amounted to any sales / conversions. It's really a long time for my poor, aging memory to remember all of this stuff that had not been important to remember until today
So yeah, I think it's a valid method of bringing some traffic and sales in, but only if your partners reciprocate the gesture. If you manage to get even 10-20 companies to return the favor it's a win-win for everyone, but the trick is to have close relationships with these other companies, otherwise I don't think you'll get many of them to place your logo on their sites. I mean, what incentive do they have to do this if you don't convince them of the benefits?