The simple answer is no: your Favorites are stored on your computer, and are totally independent on which ISP you use.
If you care about losing your Favorites, it might make sense to use File>Export>Favorites in Internet Explorer and backup the resulting (small) file together will all your other personal files to diskette, cd-rw, USb-stick or another networked computer. But, of course, that's another story.
Kees
Will I lose my favorites if I change my Internet Service Provider?

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