Hi,
Vigorous - tough to say. I think it depends on your work (are you in an overrepresented field, or a field that has many applicants who might have the higher title level applying), your impact in your job, and what your recommenders might write about. Sometimes you can have your recommenders speak to the fact that you've been put forward for a recommendation, and depending on timing you may even be able to update the schools yourself in the interview process if it comes through mid-round, but timing for interviews might vary. So, the answer depends on you and your circumstance a bit. I could see my answer going either way depending on the circumstances of the situation, but UNLESS you have concerns about spots filling for people like you, or if you can't get your recommender to talk about your imminent promotion, I think I'd wait for R2. Further details could change my opinion though so feel free to check in with one of us for a consultation if you want to discuss more!
Warmly,
Julie-Anne Heafey