Can the seeds left on the ground start new growth?
Certified GKH Gardening Expert
More than likely they will not make it to maturity if they do sprout. If you want to keep any that do germinate, then you can dig them out and transplant. Otherwise just kill them off as they pop up.
Here is an article for more information on the care of the plant: https://www.gardeningknowhow.com/ornamental/shrubs/firethorn/care-of-firethorn-bush.htm
That depends on where you live. The seeds require a 3 month cold (39F) stratification treatment in order to germinate. Here is a guide on starting them indoors. http://www.treeseedonline.com/store/p256/Firethorn_%28pyracantha_coccinea%29.html
If you live where winters are cold, you can do the stratification step by placing the soil in bags or any other container outside. Protect from soggy soil and drying out. Container mix should be damp, not wet. Move to a sunny spot when weather starts to warm. The disadvantages of leaving the seed on the ground include loss to critters, insufficient cold temperatures, seed rotting in wet soil and having to dig through tree roots to remove the seedlings at a critical time in their development. Do your own experiment and start some with the process outlined in the link.