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?
If $T(n) = \Theta(n^3\log n)$ then it is always the case that $T(n) = \Omega(n^2)$ and $T(n) = O(n^4)$.
If $T(n)$ is the worst-case complexity of an algorithm, then furthermore its average-case complexity is $O(n^4)$, always.