Is it possible to reduce a SAT problem to it's simplest form with no assumed variables in P time?
No, this is not possible, unless $P=NP$.

Why? The formula $x \wedge\lnot x$, which is always false, is technically in CNF. But, this is unsatisfiable.

Suppose we could do this in polynomial time? Then to check of a problem is satisfiable, we just minimize it. If it minimizes to our false formula, then it's not satisfiable. If it minimizes to anything else, it must be satisfiable! So we've solved SAT in polynomial time.

In terms of gates, we have the same problem: if a formula is UNSAT, then always outputting LOW is the minimal gate circuit that's equivalent.