Not technically no, at least not by default. Although html should be mostly preserved if using the markdown editor, is this conversion happening when swapping between the markdown and rich text editors?
The web clipper and the importer have access to a different note type where markup = html which can't normally be accessed.
However I did create a proof of concept plugin a while back which I thought, at the time, was kind of a very niche use case for one person but it is becoming apparent that more than a few people have asked for this, especially more recently.
At the moment it is still unpublished as I've just had so many things going on to get back into it, finish it off and publish it. It isn't something I personally have much use for and was really only made to see if such a thing was possible to prove the concept. If you want to give it a go the download is here and this post details the commands it adds that you can use to either convert a note type or create a new html note from scratch.