Can I work with an A# and not my actual green card?

The welcome to America notice is not one of the accepted documents for employment authorization. That being said, I seriously doubt that your employer would suffer any liability by paying you now rather than waiting for you to present your physical green card. The difference in time is probably a month or less unless you are requested to re-fingerprint. Also the date of the welcome to America notice should be the date on your green card once you receive it. Whether your local Department of Motor Vehicles accepts the welcome to America notice to renew your driver’s license would depend upon the state’s policy. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.  

No.  You will need to wait until you get your green card in the mail.  It usually comes only a few days later.