The duration of the shutdown is important to how the unit should be laid up. Removing the hydrocarbon from the main tower and blanketing it with nitrogen is a good practice. Similarly, doing the same thing in the gas plant should allow the unit to return to service with the minimum number of issues.
I would normally have steamed the heater coils out into the main tower and then blinded the fuel and pilot gas and any waste gas streams that are routed to the heaters. You will likely spall some coke off of the heater tubes with these actions and that coke will end up in the main tower. Removing coke from the heaters is typically a good thing. As long as you have good steam flow during the heater steam out, the heater should come back on-line with limited issues.
The only time I have left pilots on while the unit was down was when the duration of the outage was expected to be short, only a few days. If it were to go beyond that time, I would steam out the heater and blind off the fuel gas.