They can fire you if they reasonably believe from the failure to return the form from your doctor that you do not have the condition or that it is not so bad as you claim. Keep HR informed about your efforts to get a response from your doctor.
ADA matters are very complex. Consulting with an attorney now would be wise.
You can be fired while this issue is pending for any reason other than your request for accommodation.
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Your employer must allow you a reasonable time to provide medical certification of your need for reasonable accommodation. However, if you are having difficulty obtaining medical certification within a few days your employer's request, you must provide your employer with an explanation (preferably in writing) of why you cannot provide the requested medical certification until a particular date. Physicians will generally fax or scan and email a dr's note directly to an employer provided the employee has given the physician a signed a HIPAA release authorizing the Dr. to send the Dr.'s note to the employer. Meanwhile, you also need to comply with your employer's sick leave policy (if any). Check to see if you are eligible for intermittent FMLA/CFRA leave so you only need to certify once per year or until you exhaust your bank of available medical leave. If your nausea and vomiting is related to pregnancy, then you are entitled to PDLL leave of up to 4 months, which may also be taken on an intermittent basis. Of course, most employment is "at will" and you may be fired for any reason unrelated to your disability or other protected characteristic/activity at any time. Disability and medical leave law is complicated, and I recommend you consult an attorney or your union representative. You can find some information about CFRA leave and recuperative leave as a form of reasonable accommodation for a disability on the website of the Dept. of Fair Employment and Housing at www.dfeh.ca.gov.