No it is not because of classes, why dont you paste your own HTML into a standalone HTML and open it in a browser, you will see that the the footnote links are not rendered as superscripts. In order for them to be rendered as superscripts, the linked CSS files also need to be present to give the classes meaning. And if the linked CSS files are also present, calibre will use them. And just for completeness, here is an actual HTML snippet that uses classes for superscripts that will work in a browser and in calibre, because unlike the HTML you posted, it actually contains the style definitions.
Code:
<html><body><style>.ss { vertical-align:super}</style><p>A<span class="ss">superscript</span></p></body><html>