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No, the eighth class is unlikely to be usable, as the inability to use magic is hardcoded into the Barbarian class, and that doesn't suit our needs.
Heroes from the Barbarian castle, both non-magical – the Warrior and the Wanderer – will be able to use magic and will have an initial spell.
However, to learn other spells, you will have to either increase literacy through training and learn the initial spells of other heroes, or capture enemy castles, or visit various magical sites and other buildings that grant spells.
Overall, seven classes are more than enough: 3 magical, one in the middle, and 3 not focused on magic.