BY "full distant viking heritage" do you mean /nothing/ but?
If so, it would be highly unlikely that during ~900 years and > 30 generations, all of her ancestors were "pure bred vikings"
Especially since most, if not all, norse settlers were males taking local brides. So even the first generation would be "half breeds"
If you instead mean that at least some of her ancestors were viking, yes that is plusible.
OP, you might be interested in this post about ancestry in general; I'll also draw your attention to a link I posted at the bottom for an /r/AskScience AMA regarding the inter-relatedness of Europeans