Yes and Yes.... at most places, especially the mall Santas. Now if you go to one of the smaller businesses that have Santa, they usually only give you a picture (and sometimes for free) but the mall Santa places almost always offer 'packages' - and you can buy a CD with the images on it (they usually take a few pictures so you have more than one to choose from - two or three typically) and once you have that CD it is very easy to take it somewhere or upload it onto your computer and get XMAS cards made.
From what I remember, the CD is your best bet if you are wanting to get a lot of pictures made - I can't remember exactly how much it was, but I think it was around $10 or $15 for basically two pictures of your kid on it. I think that's pricey for one picture - but since this is your first baby and first time with Santa, it will probably be worth it to you.
Congrats! Christmas is so much fun when you have little ones in your life!