Upgrades from my limited knowledge - staff - in Dubai at Check in, not a chance. Onboard - pursers not allowed to do it - however if the aircraft has a few empty seat plus the purser takes a risk then maybe. As a normal (non staff) pax may get upgrade on an ad hoc basis - don't count on it. At outstations you may get upgrade at check in, if you know the guys and it helps them out, on board same as before unlikely. If you get an upgrade make the most of it because it is not the norm!!!
Bottom line Ek does not upgrade in the same way as you may get with other 'proper,long established' airlines.
In my opinion Ek as a company does not treat staff well in relation to staff travel. I am comparing EK to my past experiences using staff travel in UK and Europe when travelling with major international flag carriers.