There’s no timeline for this being enabled for delivery labels, and I don’t think there’s been a feature request submitted for this yet either.
If you’d like to put this forward as its own feature request, that would be great as I can see how this would work really well and it can piggyback on the work done for stock labels. There has been a request for Gyle Number on delivery labels but that could probably be superseded by fully customisable delivery labels… or if that’s the main priority for you could you give that a vote, as that’s a much smaller development task in comparison to fully customisable labels, to be honest!