It depends on how the battery grip is made. There are two factors to consider:

• Can one battery be removed without disconnecting the other? Some grips have a flap type door that opens to reveal both batteries sitting side-by-side and still maintaining a connection. If a grip is this type, can the access door be opened without tripping a shut-down switch? Some grips can and some grips can not. The Canon 7D, pictured below, allows either battery to be hot swapped while continuing to run on the other.

• Other grips have a removeable tray that houses both batteries. The tray itself has contacts that transmit the power and communications signals from the batteries to the camera. With this second type of grip it is not possible to install or remove a battery while the camera is being powered from the grip.

Pentax DSLRs use a hybrid of the two examples above. The Grip, which uses a slide-out tray inserted into the end of the grip, only holds one battery. Unlike most other brands, though, the grip doesn't connect through the battery well inside the camera. Instead, one battery can remain inside the camera while a second battery is contained in the grip. As long as the internal battery contains sufficient charge, the battery in the grip may be hot swapped. But there is no way to hot swap the battery inside the camera, so once it is exhausted...