That is very much crystal ball gazing stuff as it depends on availability, predicted sale of tickets in the higher cabin and EK's upgrade algorithms (which we don't know). As long as EK expects to sell tickets in that cabin, they wont issue upgrades, auto or otherwise. If I remember correctly, auto upgrade cancels at T-72 hours. And it has not always been super reliable. I have often set upgrade alerts and these have been successful in that I have received an email that upgrades were available. Within the T-72 hour window, phoning the call centre may also work (the EK call centre is in my experience one of the best - if not the best - in the industry).
As someone once said: if you really want an upgrade, working for it will improve your chances.