I'd say there is a not insignificant chance, if it is a brown dwarf. Though whether or not you would call a brown dwarf or a "hot Jupiter" a star is up for debate. In fact, two of the nearest brown dwarfs to Earth were only discovered very recently. Luhman 16 , a brown dwarf binary system, was discovered by the WISE mission in 2010. And WISE 0855 , a "sub brown dwarf", was found as recently as 2013.