Yes server will be up and running without any issues as RAID 1 virtual disk is still work even if one drive is failed. You will have data lost only if second drive get failed. 
Hello All,                 Dell Support confirmed that one of the HDD in our server Power Edge R640 is faulty which is RAID 1 configured and need to be replaced with new one.   
Hot swap of HDD in a RAID 1 Config DELL Poweredge R640 Server