The standard athletic tape starts to stretch and lose support fairly quick, and as noted above, the bulk of the typical athletic ankle tape job would be enough it would interfere with boot fit a lot.
Leukotape doesn't stretch and sticks well enough that you could probably get some extra support with just a couple heel locks on each side of the ankle. I take enough leukotape on hiking trips to do just that in case I were to sprain an ankle and need more support while on a trip. I am used to taping ankles, however, and have taped my own before when needed. The biggest risk is that the tape going across the back of the Achilles for heel locks can cause a pretty nasty blister if the angle and tension are off. That could end up causing more damage than it would help.
I would rely on your boots for support, strengthen the ankles with balance and agility exercises in the months before the trip if you are worried about it. If you do take some leukotape, I'd make sure to practice some heel locks prior to the trip to get the angles right and make sure it feels alright.