Not exactly sure what you mean but I'm guessing you're asking if Lurkr can assign specific permissions/channel access to levels and currently it can't, that's kind of the purpose of the role rewards.
You can create special permission roles that when you have it, will gain access to a specific channel. That would have the benefit of the permission not necessarily being connected to the role reward but still allows you the ability to assign it as a role reward.
And to answer your question Lurkr does not synchronize the role rewards immediately, the users will have to level up or use /syncrolerewards.