This is what happens when you go away for Christmas and swear to never give a toss about the green card process anymore. Somebody asks you a question directly and you aren't there to answer it. My apologies, Ncintu.
The answer is Yes. I speak from personal experience. I got my I-140 approved then got canned after 11 months of the I-485 process. I have since been taken on by the exciting offshore team that took over from the in-house team. Fancy that, immigrant jobs being outsourced. Such irony.
As far as I am aware, you need nothing from your previous employer. My attorney suggested I was safer to get canned than resign but that is probably just being over cautious and paid by my employer. I certainly would not worry about that.
You will need a letter from your new employer stating job title, duties and salary and stating that the job will still be there when your adjustment of status is approved. This is in case you need to send an AC21 letter - which is between you and your attorney. The consensus on this site is slightly in favor of sending one straight away, I personally cannot be bothered in case I get canned again (I'm too expensive long run for the offshoring business model), I am just going to wait for my RFE.
Otherwise you can get the letter when you need it.
Best of luck and sorry for the late reply.