You shouldn't need to worry about your dragon form.
In D2:ED health would not regenerate inside the battle tower, and you could not use the healing spell, but could use potions. If the purpose of disabling regeneration and healing was to prevent quick jumps away from combat to heal and return right away, then having potions disabled in DKS within the battle tower isn't unexpected. Actually, I never tried healing in the battle tower in D2:ED until I just went to check that before posting (I did use an intelligence potion, though, so I could meet the requirements to equip a mage set long enough to check it out).