It depends. 

If you are unable to obtain your visa and/or enter the US in time for fall classes, you will NOT qualify for CPT as you will not be in F1 status for the fall. 

Alternatively, if you are already in the US from undergraduate school and are able to get your F1 status transferred to Columbia University in time for fall classes, you will be eligible for CPT in summer 2021, whether courses are on campus or virtual for that semester. 

Any questions regarding CPT, should be directed to ISSO, not the Department.  Please read the COVID-19 FAQs.