I fly out of Auckland, and have moved here from Australia. My Mum used to be a GP (she ahs now moved onto surgery) and she used to complete medicals for Qantas.
In her opinion an irregular heartbeat or high blood pressure that can be controlled by medication should not hinder your progress to obtain any sort of employment as long as you have proven trustwirthy and experienced with your medication. This would never stop her reccommending anyone for QF.
The medical you complete is simply for a doctor to sign off that they do not think there is anything medically that will endanger the lives of the airlines passengers. A big one for EK is pregnancy (for obvious reasons). The problem you may face though is that Middle Eastern carriers actually have you undergo medical checks in your home state and then as a part of your training you must see thier doctor to confirm everything that has already been consulted on. It is not uncommon for people to be sent home from DXB and the like for not passing that particular medical. A shame but true, and do not let it be failing the drug test or they wont even pay for your ticket home.
I personally will not ever apply for those airlines, im happy working for a world class airline that does not monitor my living habbits and social patterns. That allows me to live in a country where I am used to the culture and when I go home I actually go home, not to an apartment of my colleagues.