It is true that "inte lika" can mean "not as'" However, "olika" does not literally mean "not as" (simple negation), as far as I know. It means "various" or "dissimilar", and can be used as an adjective or an adverb.
So your suggested sentence, if it is not nonsense, seems to me to mean something like "She is differently tired than he is" or "She is tired in a different way than he is."
What do native speakers think?
In both Swedish and English, it is common to omit the second verb in a construction like this. It is not wrong to add the second verb, but it is less elegant.
In any case, many writers deliberately add the verb after the pronoun in constructions like the one here, so that it can be seen that the pronoun being used is a subject rather than an object. Compare:
1. She is not as tired as him.
2. She is not as tired as he.
3. She is not as tired as he is.
1 is technically incorrect but nevertheless used by many native speakers.
2 is correct but sounds stilted to some speakers.
Therefore 3 is often used to steer the reader/listener in the right direction.