Sometimes people justify the imposition of restrictions on the length of the bonds the fact that in such way simulates a quantum mechanical effect of "freezing" of high-frequency oscillations.
Restriction/freezing of bond lengths is not usually done to make any improvements, but to allow a 2fs time step in MD (instead of the usual 1fs), so it effectively speeds up the simulation by a factor of 2.
Regarding acceleration. I routinely use 2-2.5 fs dynamics with a multi time step integrators. Therefore, I do not consider the constraints as a method of acceleration. The question only about the quality of the model.