We currently use Sunday Plus and create the service presentation at home and Sunday Plus allows us to save the presentation and associated files into a separate folder which we copy to a thumb drive and take it to Church on Sunday morning and copy that to the Church computer. Does Easyworship allow us the same capability?

Yes. You create the schedule, use the save File - Save As command to save that schedule to a flash drive. You need to check the "Pack Files In Schedule" option in the save dialog to have it save any images, videos, backgrounds, audio files etc. Take that flash drive to the Church, open the schedule, then use the Save As command to save it to the hard drive. You really need to do this as running directly from the flash drive can cause stuttering.