Y'know bringing up DBZ does make for an interesting point... namely, how many of us actually watch Dragon Ball before we watched DragonBall Z? not many I'd assume and yet we got through DBZ just fine. However that's not a perfect comparison.
First, Most of watched DBZ when we were kids when we had lower standards; we were more willing to overlook unexplained details and just watch people fight... when your audience however is teens and young adults, they might be less willing to ignore unexplained details...
Second i'm not sure DBZ called back to Dragonball as often as One piece does... i mean in DBZ we never really learn of piccolo's history as a villain, but its not important since he pretty much drops his villainous plans in the first episode thus making his past as King Piccolo and Piccolo jr. to be rather irrelevant; same goes for alot of character histories. In DBZ, The Red Ribbon army does get referenced later on with Dr.Gero, but it doesn't feel that important since Dr Gero himself never appeared in DragonBall; all in all its a rather weak call back. Heck, in some cases we were actually better off not knowing some details as some things we inconsistent... like how Piccolo was originally repeatedly called a demon only for us to found out later he's really an alien, or questioning where the heck Launch disappeared too, or having to watch the half-assed relationship between Goku and Chichi. With One piece, their are some more call backs and Oda does a good job at keeping things consistent... I don't want to go too deep into details, but some characters like Crocodile, Buggy, and Coby pop up in later arcs; some characters like Arlong, the giants, and laboon are referenced later on
Thinking about it, maybe you could just skip ahead, but you'd have to pick carefully. Season 4 seems like a good point since the alabasta arc establishes a number of details. Luffy's relationship with Ace, information about the Shichibukai, Crocodile himself, the Void century, the ancient weapons, Smoker's obsession with hunting Luffy, etc; Not to mention right after albasta we meet Blackbeard. All of which is important later on and is a lot to skip.... Stuff before the grandline, i think maybe people won't be lost without it; for the few things that are referenced i think we get flashbacks that are enough to explain them to keep people following along... Alabasta is also one of the major high points for the series
Though MAYBE they could skip ahead to the davyback fights(season 7)... At the very least Water 7, will also discuss the ancient weapons, and the void century. Though i'm not sure how well they would respond to the rest. Like do they mention enough details about the shicibukai later on that new viewers will understand their role and how they differ from other pirates? And how will they respond to Ace? I think Ace does mention that he is Luffy's brother after water 7 thus keeping viewers in the loop on his significance to luffy. Some might be confused by a number of the characters from alabasta; but if toonami takes one weekend at some point to air the alabasta movie; that won't be an issue. I'm less certain there...
Though one thing i think toonami can and should do, is just skip a lot of the filler that isn't good where they can... the marine base filler is a decent filler so they can use some time for that, but some filler arcs are not very good, and as filler they are not important, so they are totally worth skipping. Though speaking of which one filler they WOULD benefit from is the lost memory arc, since it basically summarizes the main characters backstories that we would have skipped if we don't start from episode 1
