Does an algorithm with complexity $\Theta(2^\sqrt{n})$ to solve any NP problem count as "good" and practical as any other polynomial algorithm?
Complexity is how an algorithm increases its number of steps in comparison to $n$ when we scale $n$ to a large value.

For very small $n$ , an algorithm with complexity $\Theta(2^\sqrt{n})$ can behave nearly as good as an algorithm running in polynomial time.But if we increase the $n$ , then certainly the algorithm with polynomial time will give much faster results.That's how algorithms are compared.One important thing to remember is that your $n$ is a variable related to input size and if this occurs as a power of something in time complexity then you can be sure that the algorithm is going to take a lot of time for large values of $n$.

$\Theta(2^\sqrt{n})$ is not as good as $\Theta(n\log n)$