Unlikely, as the airline will be unwilling to take the risk. It may also be wise to check with them too, with the information given to you by the surgeon/doctor.

It can be done (e.g. the poor chap who was airlifted back to the UK from Antigua after being shot on his honeymoon, but this is probably covered by his travel insurance).

I was and still am afraid to fly due to all the attention surrounding flying and DVTs. Once you have a blood clot and survive, you live with the daily constant fear of getting another one. Also, it is no fun at all having to take the blood thinning medication and the weekly blood tests.
I leave the following advice. If you have travel for a long period of time or have an occupation that requires sitting; the key is to keep the circulation flowing.

The Federal Aviation Administration requires commercial airlines at cruising altitudes to maintain a cabin pressurization equivalent to air pressure at an altitude of 8,000 ft (2,438m) or less. For travelers at risk of hypoxia, the lower oxygen partial pressure at this altitude may exacerbate underlying disease.

In patients who recently have had a sizeable myocardial infarction, airline travel should be prohibited for four to six weeks to prevent ischemia. Further recommendations should be made on the basis of exercise tolerance testing. Patients who are recovering from surgery are at higher risk of wound complications due to air pressure differences between internal organs and the changing ambient cabin pressure.

http://findarticles.com/p/articles/mi_m3225/is_n4_v44/ai_11455035?tag=untagged