...in rapid succession. Like all other text in a browser.
Not with the style -webkit-user-select:none; or equivalent.
In jQuery UI 1.7.1, there was a function $.fn.disableSelection() that would toggle all the right browser-specific CSS and attributes so that text selection would be disabled. I would recommend that the author use it during the instantiation of these buttons...
As much as this isn't my problem, there are fixes that jQuery UI could implement such as native dblclick and special jQuery events such as triple click that could be used to stop text selection.