Not necessarily. It's doubtful they'd start Jason off as a zombie capable of enduring being on fire and treading through a field nonchalantly. Even if they did, as I iterated before for me, personally, an explanation wouldn't be necessary but if one is provided I want it to be something that makes sense and is well thought out (meaning no demon slugs).
All in all, I'd prefer if they just introduced Jason again as being similar to parts two, three and four (like Derek Mears in the reboot) but with a hint of the supernatural. Then, over the course of the series you could gradually have him shift to being more zombie-esque, albeit without making it as cartoony as in the original series and without having Jason get offed (again) by a ten year old.