Can an algorithm complexity be lower than its tight low bound / higher than its tight high bound?


The worst case time complexity of a given algorithm is $ \theta(n^3logn)$ .
Is it possible that the worst time complexity is $ \Omega(n^2)$ ?
Is it possible that the worst time complexity is $ O(n^4)$ ?
The average time complexity is $ O(n^4)$ ?

IMO it is possible as long as you control the constant $ c$ , but then what’s the point of mentioning any other bound than the tight bounds?