Can you be terminated by a company if you have a doctors note putting you out of work?

Yes, you can be termianted at any time for any reason. You would only be able to file a legal claim if the time off from work was covered under the Family and Medical Leave Act (FMLA) or, in really rare circumstances, if the condition for which you needed the time off would be considered a disability under the Americans With Disabilities Act (ADA).