Do Evangelical leaders (televangelists, megachurch pastors, etc...) not consider themselves Protestants? Kind of based off this question contrasting Evangelicalism and Protestantism.  My assumption as a Catholic (which you are certainly more than free to trounce upon) is that since modern day televangelists are more than 6 degrees separated from Calvin, Wesley and Luther, that they couldn't in good faith call themselves Protestants since the Catholic Church is not weighing heavily on their consciences. 

So is this yet another false assumption?
It seems in your question your assumption is that Protestantism is something akin to Contra-Catholicism. This is not the case. What distinguishes protestants from Catholics and what identifies different denominations both as protestant is the doctrine of Justification by Faith.  

If you take that as the working definition of what is to be protestant then it is no stretch of the imagination to think that all of the major evangelical leaders would classify themselves as protestants.

As a member of an extremely large non denominational evangelical church I can say with some authority that we believe and promote the doctrines 'priesthood of all believers' and 'Sola Scriptura' both of which are distinguishing beliefs of Protestantism. I would be shocked if I learned other similar churches did not believe the same.

Have evangelicals (and thereby many protestants) and Catholics moved closer theologically since the reformation? Perhaps; although here is a recent article that discusses remaining tensions between the two (specifically reformed theology).