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Evening Chris,
Yes indeed, you’ll have no problem creating a new site with Blocs, then uploading via your ftp to your existing host. I’ve done this many times now.
As @DaveC commented yes you can. If you’re not happy with the hosting plan price it would be a good time to look for a new hosting service. Lot’s to choose from, if you’ve only got one site it should not cost much to host it.
Casey