If you look at a President or Provost's bio, you will find that all of them started off as an assistant or associate professor and went up the ranks until they got full professor. They then usually start taking leadership positions within their department (i.e., Director of Undergraduate Programs, Assistant Dean of Research, etc.) and then eventually become Dean. It is then that they can begin to look at applying for positions of Provost or President.
Also, if you look at most President or Provost's bios, nearly all of them have a Ph.D. in their specialty. Most of them have extensive experience in teaching and impressive lists of published publications.
A Ph.D. in "Higher Education Leadership" will not give you a leg up... what will give you a leg up is many many many years of experience as a professor, hard work, and ensuring you publish a lot of research. President/Provost positions are far and few between and are extremely competitive.
Go to higheredjobs website -- nearly all colleges/universities use this site and take a look at the requirements for president and provost positions.