You wont see a champion of Khorne with a Manreaper nor would you see a champion of Tzeentch with a Blissgiver. Why? Cause their gods would probably disown their unloyal asses. Gods specific weapons exist for a reason, they are alligned to the said god and people who arent their champions are not going to be wielding them, ever. If you read the list above theres more than enough of undivided weapons, just like theres more than enough god specific ones per god. So theres no reason one should trample over lore (as if Games Workshop would even allow it).
I understand that you won't see a champion of Khorne with a Mapreaper, but, we don't have any God specific troop choices either. All available Legions are undivided.
And in those legions exist warbands that are not undivided. Black Legion for example: http://warhammer40k.wikia.com/wiki/Chosen_of_Abaddon and their respective warbands are each dedicated to a single god even if the Black Legion itself is undivided. They already said boons and mutations will be ingame (http://forum.eternalcrusade.com/threads/mmorpg-com-dev-q-a.1163/) and if you watched the AMA when they responded to a related question god specific stuff is going to be in too, just that it will probably be not so fleshed out since they said they will expand on it post launch. Also they said they will add more legions later on (they still didnt put out the vote for the fifth legion that will appear at launch) which brings with itself god specific troops (you can see their intent to add such units post launch on Patricks profile).
Here also read up on the compilation of info up until now in this thread with sources: http://forum.eternalcrusade.com/threads/compilation-of-info-about-eternal-crusade.1959/ And ofc i advise watching the 4 AMA vids on twitch: http://www.twitch.tv/40kcrusade/b/426139667 Enjoy your stay on the forums fellow Nurgleite (if i read the avatar correctly).
There are both kinds of weapon in lore undivided and specific to a chaos god. If you are undivided you cannot access the specific weapons and undivided has access to undivided, tho for game balance sake I would allow that worshipers of specific chaos god can have picks of related undivided weapons, like melee weapons only for a khorne follower from the undivided pool, while a Nurgle player could also have some melee weapon they would probably be more restricted as they could potentially have more trinkets (like special wargear) related to big papa nurgle + nurgle only spells if sorcerer path is chosen, which khorne doesn't have.
If they are included, for the followers of Khorne, The Hellblade could be a weapon. You know, the weapons wielded by the Bloodletters of Khorne
IMO Daemon weapons should be in game, and I like the OPs idea of each weapon type can progress etc, but I do think it should be a long old trek to get there!
Abaddon the despoiler had to do specific things for the chaos gods before they led him to the daemon sword drach'nyen, so it would be cool to see a specific series of quests that lead to the attaiment of one. Wanting to play night lords however, I'm going to go down the no gods route for me, but I'm not against the inclusion of them