While candidates are not judged based on their immigration status but if you need an H1B to start your job, you might be removed from the list as acquiring H1B requires time for the department. Departments would like to hire you while you are on your OPT or OPT extension and apply for H1B after one semester. As academic institutions are capped exempt, you will most probably get your H1B without any problem.
In many of applications, applicants have to answer these two infamous questions.
Are you legally allowed to work in the united states?
Do you now or in future require sponsorship from school?
I have also seen a lot of department heads personally reseach out to candidates to ask these two questions. The rule of thumb is that, smaller schools do not want to go through trouble of sponsoring you and prefer candiates with valid status.
My recommendation to my international applicant is to apply for Green Card through EB1 or EB2-NIW to enahnce your chances in getting jobs in both academia and industry.