Feasible to capture data to/from a 1970s RAM chip?
There is no need to emulate the RAM itself unless you want to be able to change the data in it.
To capture the write data you have to watch the /WR, CS, address and data lines. When the /WR and all CS inputs are active you read the address and data lines, then store the data in an array with the address value as the index. You will also need to synchronize your reads with the CPU. This can be done by waiting for the address lines to change or by monitoring φ1 or φ2.
Timing will be tight. At 1 MHz the 6800's bus cycle time is 1 us, but it can take up to 270 ns for the signals to stabilize, and if RAM access is gated with φ2 you may have less than 500 ns to respond. Worst case scenario is when the 6800 gets an interrupt and pushes 7 bytes in succession onto the stack, then your device will have to read and store each in byte in under 1 us.
An AVR based Arduino could probably do it, but the standard Arduino functions are far too slow so you will need to write some carefully crafted C or assembly code. Interrupts are too slow, so you will have to continuously poll an I/O port. AVR executes most instructions in 1 cycle, so a 16 MHz Arduino should be fast enough.
CPU load can be somewhat reduced by adding a bit of external logic. A few gates or a comparator IC (eg. 74HCT688) could be used to decode the control signals, then the AVR only has to test one pin. This also reduces the number of I/O pins required.
The Raspberry Pi has a much faster CPU, but if the OS is active it will suffer from 'random' interruptions, and it needs level shifters to work with a 5 V bus.