Will that require a new download of the blockchain?
No. However it will require that it rebuilds the databases, but that is supposed to happen and it will be a lot quicker. The databases are also a lot smaller now. However, you will have to go to the armory data directory and delete the databases folder. After you install 0.94.1 but before you start it up, go to ~/.armory and delete the folder named "databases". Then start Armory.
Also, any ideas why Armory (0.93.3) isn't telling me there is a new version available?
That is probably the downside of ubuntu, i used to had that same problem with electrum.
You just don't know what you are talking about.
The reason Armory doesn't tell you about the new version is because the new version is not developed by Armory Technologies Inc (ATI) but rather by Goatpig (a former ATI employee) who was given control over Armory. However ATI controls the announcements server and not goatpig. The announcements system has also been down for a while and it was removed in the latest version.