Is this possible to solve 3SAT in O(n^24) time and O(1) space?
You are correct in your assumption that your algorithm correctly identifies some unsatisfiable instances, but for the general case it does not work.

For instance, you can always rewrite a clause $\{A, B, C\}$ to the equisatisfiable clause set $\{A, X, Y\}, \{\neg X, A, B\}, \{\neg Y, B, C\}$. To see this, observe that you can always recover the original clause through resolution. If applied to say, the first clause in the above example, this will already break your algorithm.

Maybe someone with more knowledge on SAT can give some more insightful information.