I moved away from my hometown longer ago than that and had no problem depositing cheques in branches other than the one with which I was registered. It may depend on the bank you are using, or possibly even the method of deposit and the branch's ability to provide the resources for it.
I think the whole concept of “branches” is basically gone.
Except if the bank sells off a region (e.g. merges with another bank, but is required to sell off some operations for competition reasons), then you’ll end up following your home branch.
It used to be that the home branch would technically be responsible for verifying cheques, but i’m Sure that’s all centralized now too.
