This has been tried. I think the IBM System/360 could do arithmetic directly in RAM.
Here is an example of such an instruction from the
"AP, Add Packed (Decimal) The data string located at the storage address specified by operand-2 (b2+d2) is added to the data string located at the storage address specified by operand-1 (b1+d1). Operand-2 remains unchanged."
http://www.simotime.com/asmins01.htm#AP
Now, how this was actually done in hardware I don't know, but I would not be surprised if hidden registers were involved. So, maybe this is not really an example that fits the original premise of this subthread, but I think it is interesting nevertheless.