According to a block diagram showing all the data buses of the Dreamcast, it clearly shows there are no external buses that would support memory or processor upgrades. So there will be no possibility of a RAM cart with the Dreamcast. Considering the hit or miss aspect of upgrade peripherals, this is a good decision by Sega to not even make it something to consider. The Saturn RAM cart was succesful, but it had the strong support of both Capcom and SNK and made its appearance near the end of the Saturn's cycle. Sega is better off with slightly less than perfect graphical ports than a fragmented market. You can view the diagram below.

Thanks to DC Tech.