Not in the slightest. People ask for quiet rooms all the time. On a scale of 1-10, the level of suspicion associated with a request like this is somewhere around minus -286.
It's always a good idea to telephone the specific hotel you are interested in during quiet times (often during overnight hours) for finding out when they have the most vacancies and fewest guests, because that's when you get the lowest rates and best room selections.
Their job is to answer your questions and to sell rooms. The only questions they should be asking have to do with how to better accommodate your needs.
A suspicious employee is a fired employee, and a suspicious hotel in a desperately competitive field is a hotel which will quickly find itself out of business. Beggars can't be choosers, and hotels are begging for business.