yes, you will be deported if your asylum application gets rejected even though you have F-1 status because primary basis of F-1 status is "intention to return to home counrty after completing study". So. applying for any immigrant status (either, asylum, immigrantion thru work or family) shows your intention to migrate which in turn disqualify you from holding F-1 status.

So, after getting your asylum application rejection, your F-1 status will also be voided ans you will be illegal and deported.