Does having a job at a grocery store count as occupation

Yes, it would.   Are you referring to the Occupation field in the My Info/Personal Info section?   That field is asking for whatever job you do for a living that you derive the bulk of your work income from.    That is the occupation that will be printed on your tax return.  That's just an informational field mostly used for statistical purposes and analysis. 

However, "job at grocery store" is not a very specific way to describe your work, however, such as grocery stocker, grocery cashier, grocery clerk, grocery bagger, customer service, produce manager, etc., or if you do several things and want it more general, such as grocery worker, grocery employee, etc.  It's really up to you--whatever you call yourself when you tell friends/family what you do.