As with most questions concerning an individual’s personal training, the answer to this is “It Depends”. It depends on how fit you are now and how difficult the climb of Mera peak is for you. For someone with a very high fitness base a climb like Mera peak will not be much different than their typical weekly training load and they will recovery very quickly and be ready to start back to normal training after only the travel days. But if the the Mera climb entails more work on one day then you do in a week and you have to do this day after day then chances are that you will need the 2 weeks you are planning.
Only you can know what your current level of fitness is and how much work you can handle before needing a significant rest/recovery period. I suggest being quite conservative when you come back from Mera. Take a week off. The then go do one of the harder workouts you did in the final weeks before Mera and see how you handle it.
Scott