It could work, but it would probably be better leaving it until you could include at least a few non-English players on merit.
The one problem with your schedule is that you've got two consecutive years when the southern hemisphere is hosting a tour. Might it be better to have the GB tour the year after the world cup? This would be right at the start of the world cup cycle, so the individual nation's preparations would be affected, neither would it get in the way of any world cup qualifiers (if they are brought in again). After that each nation has a clear run through to the next world cup in which to get their preparations right.
And we could have the GB tour to the south, Aussies and Kiwis up her for the 4 nations, then back down there for the return.
The only problem now is to get those non-English players up to the standard...
And in that vein, why not take up the idea that I think RoughyedSpud put forward. If, as expected, the number of imports reduces over the next few years, and the Exiles team is no longer feasible, why not re-introduce the Other Nationalities team. That was originally made up of Welsh, Irish and Scottish players when there weren't enough to make strong enough sides for each nation. Include the best professionals from each nation (call them Other Nationalities, Celtic Nations or whatever) and see if they can give England a decent challenge. When and if they can, or if some of the players approach the level of England's performance, then reconsider introducing Great Britain and Ireland.
Yes, I'd mix it up a bit an alternative England/GB traveling to Oz. It was just something off the top of my head.