Wordpress - Is wp_is_mobile() effective?

Yes it works well. It's a very simple function but never found a mobile device not recognized by it. It recognize the 90%+ of mobile devices. Main difference from mobiledetect.net is that doesn't differe from phone and tablets.

See the code

Yes, the wp_is_mobile() works well, but you can run into problems when using aggressive caching systems, such as fastcgi, proxy cache, etc. that skip the php execution.

If that is the case, I would recomend some client side (javascript) detection method that is loaded for both mobile and desktop browsers.

It is a shitty idea to use that function. Device identification should always be done at the client side, and user agent is probably the worst way to identify whether a device supports a feature X or have a form factor Y.

You start using it when the site is young and then your site grows and you decide to cache your HTML and boom all your device detection code stops working..... Better not to walk down that ally in the first place.