If USCIS approved H1, generally consulates cannot deny a visa except when they find definitive issues of impropriety. Problems could arise if the company is small, if the company is a consulting company and there is no real project yet, if it has been only 1 year since the person got out of college and still got H1 approval where as the requirements ask for few years experience etc..
F1 denial should not affect H1 unless the denial is because of some fraud. Most common F1 denial is because they think the applicant is a "potential immigrant". That is not an issue with H1.