This doesn't seem to me like an accurate characterization of NSA. In a synthetic treatment of the reals, we posit some axioms about the reals, and we simply assume that there exists a systems that obeys those axioms. In a constructive description of the reals, we build them up using Dedekind cuts or whatever. The situation is exactly the same for the hyperreals. One can approach the hyperreals in either a synthetic style or a constructive style. It's certainly a matter of taste in terms of your own work. However, when we educate other people in mathematics, IMO it's irresponsible not to help them become literate in the common practices of science and engineering, which include the manipulation of infinitesimals.