Sending a paper which is under review for showing competency in order to find a paid sabbatical leave
I'm not familiar with paid sabbaticals for students. They are normally granted to tenured academics, at least in my experience. But for any sort of leave from your studies, I don't think there is any issue about revealing your "work in progress" to potential employers. Since it is under review you might be interfering with the blind review process but that is really for the editor to manage. The work is yours until you give up copyright to a journal. 

But, you should check the policies of the journal. It may be that in submitting, you are implicitly agreeing not to share the work during the review process. If that is the case, however, your option would be to withdraw the paper. 

It is also possible that you would consider asking this question of the journal editor and ask for advice there. It might nudge the editor to make a decision, whether favorable or unfavorable. 

But prior to publishing the work, it is best to label it as "in progress."