not unless vs. generally not unless

thank you for your attention.

My question is about the difference in meaning between the following sentences:

(i) "A novel is not considered unless it successfully engages the imagination of most readers"

(ii) "A novel is generally not considered unless it successfully engages the imagination of most readers"

For me, (i) means a novel is considered only when it successfully engages the imagination of most readers.

However, I am not sure whether (ii) means the same or not? Could I interpret the (ii) as "A novel is generally considered only when it successfully engages the imagination of most readers".

Thank you very much for your time.
Leon