Since this rolled out gradually, we shouldn’t see a precipitous drop in rankings for sites that aren’t mobile-friendly. The relevant algorithm is a per-page signal, which means every page on your site will be crawled and indexed, and that takes time.
Regardless of the ultimate effect this new update will have on your site, it’s worth stating again: Having a site that doesn’t provide a good experience for mobile users is a risk not worth taking. According to Google, an overwhelming majority of people with smartphones — nearly all, in fact — use their phones to search for local information. With simple options available, such as using responsive themes or templates for your website, almost every business can go mobile without breaking the bank.
As Google noted in its announcement, even if your site isn’t mobile-friendly but has relevant, high-quality content, you can still do well in rankings. Keep your focus on the intent of search queries and you’ll never go wrong.
If you need to check out how mobile-friendly your site is or get advice on how to make your mobile site better, visit Google’s mobile guide and then take the newly-updated mobile-friendly test (expected to eventually replace the original test). You should soon also see a link to the updated testing tool within the Search Console mobile usability report for your site.