The simple answer: yes.
If your family was from an area that was popular with the New England “planters” , Revolutionary War era Loyalists, or economic “Late Loyalists,” they may have roots in colonial Massachusetts.
If you want to identify Mayflower line ancestors, focus on using established techniques for researching planters, loyalists, or late loyalists. These techniques should help you trace out your family to at least that generation.
From there, focus on getting your family back across the border and to Massachusetts. Given how well documented the Mayflower lines are, once you’ve identified the family in Massachusetts, you should be able to determine if they do – or do not – link to a Mayflower ancestor.