No - dame refers to fact that run by a woman - generally for those between 5 and 12 - all students in one class !

Some records exist (and are in Manx Museum) but generally not until the 1872 act put schools under national control.

Often the school still exists it will have old registers but like many such records they were not archived so a bit of luck is required.

However ask yourself what you expect to find from such records ?

For schools in general - see http://www.ee.surrey.ac.uk/Contrib/manx/catalog/d426.htm
I will add the Ramsey dame school to a link from that page in next few days.