No, you're not overestimating it but it very much depends on the problem and constraints. It's good to do the d^n search space check to give you a feel for the starting size of the problem but if your problem is heavily constrained i.e. the constraints make finding a solution hard, then propagation is very powerful.

Consider variables a[1:1000] and b[1:10] and constraint a + b = 10. A good solver will use propagation to reduce that to a[1:9] and b[1:9] because there is no support for a >= 10 or b >= 10. Even reducing one extra value from a variable's domain is reducing the search space by a factor so propagation over tight constraints is extremely powerful.

Most arithmetic constraints like those used in your program will use bounds consistency (find support for the lower and upper bound values). Special constraints such as "all different" have their own propagation algorithms that efficiently remove potential values from the domains of multiple variables. These are known as Global Constraints.