Seasonal jobs that might turn permanent

A staffing agency says some roles convert to permanent after 4 weeks. I have read a lot of threads here and could not find my exact situation. I would like to avoid a gap in my résumé. Is it worth applying to several at once?

Keep everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.

I was converted after one season because I showed up every day and volunteered for extra shifts. Managers remember that.