Most on-die embedded DRAM is one cycle away for a whole word (I'm not sure about arduino but I'll bet it's in the same ballpark). This uses a 500 ns pulse for each bit, so reading a 8-bit word would take 40 clock cycles (at 10 mHz)
No, you can't get anywhere close to modern DRAM with this type of core memory. FRAM chips [1] which use the principle of Ferrormagnetism to retain data while power is off are fairly quick however. They can replace the typical serial flash or EEPROMs you might use to save settings, and they have the benefit of unlimited write cycles and faster (than flash) write times.
The sheer size of the core memory, e.g. measured in millimeters, will prevent it from having access times in comparable orders of magnitude as silicon-based DRAMs, whose dimensions are measured in micrometers.
Cool project, btw :-)