JQUI was not meant to be confined to non-mobile browsers, it was just designed with desktop web browsing in mind. Will it work with mobile? Maybe; it's not technically supported, but that doesn't mean it may not work. As for the widgets, some may be hard to use on mobile devices. It really is up to you to decide. I wouldn't expect a site designed with JQUI to work on every mobile device, but if you are only targetting say iPhones and it works for you, then that's great.
With that being said it really is more of a trial and error, you will probably have to do some custom development as well (css, js, and whatever else you need). to make it play with with mobile devices.