possible. But unlikely, in the first couple of weeks at least. And remember, it all depends how the birth goes and what type of sleeping pattern if any your baby might have. Some people may have a very smooth quick labour which they bounce back easily from, have a baby that settles into a nice relaxing sleep pattern from the outset and all is calm and chilled, and there is time for 'you' if you really want or need it.
Sometimes, people have long, or difficult or just tiring births, which they take a little while to recover from, or a baby that has colic, or feeds hourly or does not settle well. And then any 'you' time goes out the window. And you get lots of people with variious degrees of those things.
with DD, i had a reasonable amount of 'me' time which was fortunate as my mother was ill and we spent a lot of time travelling, and visiting hospitals and whatnot, she was content and happy to be stuck in a car for hours on end. My DS, now 10 months, fed 1-2 hourly from the outset, for the first 3 months, and then at growth spurts, and while content when not feeding, mostly fed, so any thought of 'me' time went out the window. When I was not feeding, i was sleeping.
I think, hope for some, but do not rely on it.