When you add any number of the original cuts (presumably as constraints, rather than lazy constraints or user cuts) and then restart the solver, CPLEX will go through a presolve step, the results of which may be different from the original presolve due to the presence of the extra constraints. It will then solve the root LP, the solution to which will likely ...
CP-SAT uses a SAT backend. But at any moment, just like with SMT solvers, the full model is never fully represented using clauses and Boolean literals. I recommend looking at the CPAIOR 2020 masterclass on CP (on YouTube) to get a better understanding of the architecture of the solver.
Unless you turn off the presolve step, CPLEX will eliminate the variables that are locked at zero during presolve. So the answer to your second question is that presolve may take slightly longer (but the difference will be too small to notice) and the actual branch-and-cut phase will not take any longer than if you had omitted the variables yourself. The ...
I recommand the Model Building Book by Williams and here you may see the examples in OPL.
Let me add some OPL links:
How to with OPL ?
Tips and tricks
OPL and Excel
Making Optimization Simple