Seasonal jobs that might turn permanent - first time posting

A staffing agency says some roles convert to permanent after 8 weeks. I am in Tucson, in case local advice matters. I would like to avoid a gap in my résumé. Is it worth applying to several at once?

Thanks for writing this out. I went through something close to it 14 months ago, and it got easier once I kept a simple log of every call and form.