Is it possible to delete the entire blog except the SQL database and then upload the new 2.66 version and then import the database into the new blog scripts and rebuild the site?

yes, but unecessary unless you have some special reason to do so. Just upload the MT files (either from the upgrade package or the full package) and continue on. no need to reload the database.

I would feel better wiping out the entire MT directory and uploading the new. How would I rebuild the blog after doing so?

well, if you insist, then just delete the files in the directory where you originally installed MT (you might want to keep mt.cfg around...it hasn't changed with the new version anyway), upload the new version, log into MT and hit rebuild.