Sure, but a couple of cautions:
a. The SSR needs to be one that will accept 120 VAC as a control input, i.e., it is
NOT the typical SSR that one would use in a PID situation which has a ~12 VDC polarity sensitive input. Certainly Chris' Coffee sells the correct SSR.
b. I would de-solder the heater relay off the board - you do have experience on me here

c. The pstat likely has two wires attached. One originates from the Gicar and is "hot" as long as the machine is on and water levels are OK - at least that's how I think your machine is set up. Usually this is connected to the "C" terminal on the pstat but ya need to verify all of this. The other pstat terminal goes back to the Gicar board also. Use some double male connectors and lead two 16 gage wires back to the new SSR - not polarity sensitive.
d. One side of the SSR needs power when the machine is on - use 14 gage wire, maybe 12 gage to be really safe. The other side of the SSR gets connected to the wire from the Gicar that previously fed the heating element.
Take PLENTY of pics before and after.
If you have any doubts whatsoever, give me a call at 301-587-5033.