It makes a difference only in the sense that being compelled to pray and being allowed to opt out are different. Introducing "quiet time" because you believe in order to fix the problem with kids wanting to pray but telling them it's actually "quiet time" where they can do whatever they want is no different than introducing "prayer time" and telling kids they can do what they want. The intent remains, however much you're trying to pretend it isn't there. What is especially transparent in your "quiet time" proposal is that it obviously encourages Christian prayer. Buddhist or Hindu chants would definitely not be quiet, Muslim prayer requires a fair degree of physical space and a prayer mat, as well as a way to indicate qibla(direction where Mecca is), and Jewish prayer should be communal and ideally involve a quorum of 10 men who've been Bar Mitzvaed. How would you accommodate these religions?