I've never heard of/seen a poster being included, I thought one of the Jags I've had over the years came with some sort of Jag merch catalog. I bought it secondhand so who is to say if it was original. I still have a NOS unit from Best, but it's sealed. I know Bradley throws in some extras with those. In true failing Atari fashion I'm sure this stuff varied. There's also that Japanese set that included AvP and Japanese manuals.
A and B share the same pin on the Genesis as do Start/C, it's a difference of low or high. I would doubt this adapter will let you use a Jag controller on a Genesis with all buttons functioning correctly.