The named character references added in HTML5 do not work cross-browser, though the support is relatively widespread now. Generally, there is hardly ever any reason to use them (as opposite to references defined in HTML 4.1, which are well supported).
Quite independently of this, the characters themselves (no matter whether entered as such, as named references, or as numeric references) need to exist in some font in the system and the browser needs to know how to find them. There is no list of characters with crossbrowser/crossplatform support, since each system has its own fonts and many browsers have specialities in using fonts.
To make characters appear in (almost) all systems, you would need to use web fonts (downloadable fonts), which come with problems of their own. See my Guide to using special characters in HTML.