There are two kinds of ESD bags, conductive/shielding bags (the black or black-meshed ones) and dissipative ones (the slightly rancid smelling pink ones).
The conductive bags, as long as they are well closed, are suitable to storing ESD-sensitive objects inside packaging that can generate ESD (plastic bags, styrofoam...) - the dissipative materials are merely meant as a packaging that does not generate static charges in places that are already well ESD protected (eg inside a conductive bag and/or metal container).
That said, your average computer mainboard is very likely full of ESD protection built into the circuitry itself (eg zener diodes built into ICs), since these are often handled in very non-ESD-safe locations. Still, relying on such circuitry tends to wear it down until actual damage will happen.
Putting a computer mainboard into a conductive bag, if it is of style where all surfaces are conductive, directly could lead to rapid discharging of the RTC battery.