There are many articles on the web on transformational leadership and these are applicable to many/any contexts. But to answer your question in summary, i believe YES, transformational leadership is much needed for student modernity. Epochs and Eras are continuously changing and old leadership styles will not suffice nor be proactive enough to deal with modern 'game-changers'. Students are the leaders of the future and coupled with their technology savvy/abilities, leadership styles will have to evolve in order be cognisant of this. I personally have an interest in 'proactive' leadership, rather than 'reactive'. The aspect of 'proactive' can fit 'transformational leadership' adroitly.
If you are planning a study, perhaps a good mixed method study will suffice. A quantitative approach can entail correlation and regression component to examine the relationships influence between 'transformational leadership ' and 'modernity' whilst also supported by inductive qualitative thematic analysis.
With all due respect and humility, I think that it is not the style of leadership that needs to be changed in schools to improve the student's modernity... what we need to change is our concept of leadership.
In my book "New reality, New leadership" I try to explain that the concept we have of leadership is wrong, in which we assume that economic, administrative, and managerial positions must be related to it; in the same way that we assume that, by simple linear logic, the professor is the leader of the classroom.
If we really want to improve the student's modernity at the present time, we have to understand that leadership is an attitude that could be developed, yes, but it requires support to sustain itself, so we must focus on raising awareness of the common benefit and critical thinking, this will allow -regardless of the type of leadership that is practiced- those who experience it to be more demanding and less complacent in front of it.