Obviously, the artillery training was not stopped in the period from 1801 to 1808. At least there was a class at the Guard artillery for the Guard Artillery NCOs who wanted to become officers. NCOs of the line artillery also could become officers by passing an exam at the Artillery Department. Most artillery company commanders graduated either from the Artillery and Engineer Cadet Corps or from the Land Cadet Corps, so they were able to teach their subordinate officers well enough.
Before Paul started to reform the Cadet Corps, most officers graduated from the Land Corps became staff officers, or engineer officers, or infantry officers, or cavalry officers, only a few became artillery officers, while most officers graduated from the Artillery and Engineer Corps became artillery officers or engineer officers. After the reform was finished, the educational programme in both Corps had become nearly the same, and any officer graduated from either Corps could become an artillery officer. I haven't got any exact information on how the educational programme in both these Corps changed during the period.