Yes, it is possible to BCC the CRM from your mobile device. To do so, you'll need to manually enter the address YOURHUBID@bcc.hubspot.com into the BCC box of your email. You can find your “Hub ID” in the top-right corner of your CRM account.
Currently, we do not have automatic (check-box) "log in CRM" functionality in mobile email clients, so this is the best way to accomplish this from a mobile device.
You can also use this same method to forward email replies to the CRM using the address YOURHUBID@forward.hubspot.com