Simulating a combinatorial network
Yes.  Simulation is straightforward and doesn't require any special ideas: it can be done directly, by just executing the circuit one gate at a time.

The algorithm to simulate a combinational circuit is completely straightforward.  Given a combinational circuit $C$ and an input $x$, it is easy to compute the output $y=C(x)$, simply by simulating each gate, one gate at a time.  Each gate in the combinational circuit is either an AND gate or an inverter.  Both can be implemented in software.  So, to simulate such a circuit, you just iterate through the gates in topologically sorted order, compute the effect of each gate, and store the value of its output wire.  This is a trivial, linear-time algorithm.  There's no need for SAT solvers or anything fancy like that.

Of course, when you compute the output of the circuit on some input, it's straightforward to save the output anywhere you like.  If you only want to test the circuit on certain inputs, just do that.  If you want to compare the output of the circuit to the known-correct output, you can do that: it's just an equality test.



Alternatively: A combinational circuit is a special case of a sequential circuit.  A sequential circuit is allowed to have both combinational logic and memory (e.g., registers).  A combinational circuit is the special case where you have no memory (e.g., no registers).  So, in principle any method for sequential circuit simulation already provides you a way to simulate combinational circuits.