It may help you to get cheaper quote, but it does not look nice when clients do that. If someone makes effort to visit you (at no cost for you) they deserve couple of minutes to discuss your plans and budget in privacy of just you and tradesman. Just my opinion though.
In my opinion this would not be the best way forward as it may cause the client-tradesman relationship get off to an awkward start. My advice would be to make time and have each tradesman visit at say 1hr separate time slots so as to not cross. In my opinion.