If you're allowed to do an exponential amount of work, then you might just solve SAT on all formulae of that size. Then you create an exponential size lookup table. Now when you're given the instance, just look it up and you've solved the problem.
On the other hand, if you insist that the stored data should only be of polynomial size, then the question you're asking is whether 3SAT is in P/polyP/poly. The notion of unbounded pre-computation based only on the input length is nicely captured by the concept called adviceadvice in complexity theory. The "/poly" after P basically means that the polynomial-time algorithm has access to a trusted polynomial-size string which depends only on the input length and not the instance. The advice string itself may be very hard to compute. All we need is the existence of such a string, not necessarily computability.
It is not known if 3SAT is in P/poly, and it's not known if this implies P = NP. However, it does imply that the polynomial hierarchy collapses to the second level by the Karp-Lipton theoremKarp-Lipton theorem.
Lastly, P/poly has a nice intuitive description. It is the set of problems that can be solved by a polynomial-size circuit family.
