Is this possible to solve satisfiability by using Quine McCluskey algorithm to simplify the whole given boolean formula by simplifying subformulas?
If you're planning to apply this to each subformula with 16 variables:

No, that doesn't work for the same reason given in ratchet freak's answer.  As the Wikipedia article states, Quine McCluskey is functionally identical to Karnaugh maps, so your idea has the exact same problem.



If you're planning to apply this to the entire formula:

No, that doesn't work.  Quine McCluskey outputs a DNF formula or CNF formula.  That alone doesn't tell you whether the resulting formula is satisfiable or not.  You haven't said how to test whether there is a "contradiction"; testing for a "contradiction" is exactly the problem of testing satisfiability, so this hasn't gained you anything.

In any case, Quine McCluskey takes exponential time in the worst case.  Therefore, this approach is inefficient for formulas of any substantial size.  As far as asymptotic worst-case running time is concerned, you might as well just enumerate all possible assignments and see if any of them satisfy the algorithm -- that also takes exponential time.