Seasonal jobs that might turn permanent (Raleigh)

A staffing agency says some roles convert to permanent after 5 weeks. I worked as an event coordinator before this. I would like to avoid a gap in my résumé. Is it worth applying to several at once?

Keep a list of supervisors' names. A reference from one of them helped me land my next job.

Apply to several. Start dates and schedules change quickly and having options helps.