I don't think you ever stated what the surgery was. Pig valve? Coronary Artery Bypass. Whole Heart Upgrade? Bionic Heart?
I do think there will be benefits of getting the new rig early. Getting comfortable riding it. Mirror? Panniers? Flag? Getting in & out? I like those steering handle upgrades posted earlier. Tuning? Etc. Although, you can certainly leave some for later too, as you're sitting home trying to occupy your time.
It sounds like the surgeons really don't want you bumping your sternum, and I'm not convinced that cycling will be particularly better than driving a car.
At the same time, some activity will be useful. Keep moving. Avoid blood clots, etc.
But also go by the guidelines of the docs and nurses.
I wouldn't avoid buying the trike on the off chance that you won't wake up as the value won't crash overnight, and it can always be re-sold.