It will be a pain but you could do it if you really really wanted to.
I'd advise getting a swivelling car seat as in whatever car it makes it loads and loads easier especially when they get bigger.
We've got a Recaro seat (
https://www.recaro-kids.uk/zero-1-elite-i-size.html) which had a separate infant carrier which clipped in to the main seat which was really handy when my daughter was really small, you could rotate the main seat to face you and then just pop her in in her carrier. That'd be as easy as you could make it in a 2 door car.
But once she was about 6 months she's in the main bit of the seat and you'll be lifting them in until they're at least 18months old i'd have though and in reality you'll still have to lift them and put them in quite a bit of the time when they're grumpy, sleepy or just generally don't want too.
It comes down to how much you're willing to put up with, i couldn't imagine doing that myself if it'd be the main car and not a once a month thing. Just the big doors of a 2 door car would make it a huge pain in all the places you'll need to go with a baby, as has been said good luck ever getting into baby spaces at the supermarket, 80% of them at my local Tesco are now disabled spaces with about 6 token baby spaces in the far end which are usually taken up with either chavs or blue badge holders.. Plus you'll need a back made of steel to keep twisting to put them in and out without bashing their head on the door frame or seat all the time especially when they're kicking off and don't want to be strapped in!
Edit: yeah regarding the stuff you need, whatever you have in your minds eye now, at least double it if not more. Babies come with so much stuff its not even funny. prams are huge, you need a bag of stuff for nappy changes etc, then toys, coats, blankets and i don't even know what else but it all seems to really eat up the space. Our Toyota Avensis estate is always pretty much full, if you do the food shopping you really struggle to fit the bags in on top of whats already in there.