Complexity of pattern matching for modus ponens logical conclusions
This boils down to the question of whether there exists a polynomial-time algorithm for your matching operation.
If there exists such an algorithm, call it $A$, then the answer to your question is yes: given an augmented Turing machine that uses these operations, you can convert it to an ordinary Turing machine by simulating those operations using $A$.  This blows up the running time by at most a polynomial.  (Invoking a polynomial-time subroutine at most polynomially many times leaves with a running time that remains polynomial.)
If there is no such algorithm, then the answer to your question is no: the matching problem can be solved in polynomial time (indeed, constant time) on an augmented Turing machine, but cannot be solved in polynomial time on an ordinary Turing machine.
I'm not clear on the definition of your matching operation, and I'm not an expert in computational logic, so I don't know what is the computational complexity of the matching operation you have in mind.