No, a single simple PID loop can't "know" the heat capacity of your entire mash+tun+RIMS system, and how fast it can ramp the mash temperature for your flow rate through the RIMS heater.
What you need for that is an adaptive nested control loop type system. This is somewhat similar how the brew-pi type fermentation controllers operate - they control the temperature of the fermentation chamber using a control algorithm that is somewhere between a simple thermostat and a PID loop (thermostat with overshoot prediction). The temperature of the fermentation chamber is set by a PID loop controlling the fermenting beer temperature. To do this you need two temperature sensors, one monitoring the beer temp, and one monitoring the fermentation chamber temps.
In principle, something like CraftBeerPi or the other more advanced controllers could do this, but it may not be worth it, given the time it would take for them to learn for each different batch vs the time taken to actually mash. I guess you may be able to use the recipe to predict the mash volume and thus predict the heat capacity of the mash+system, and a flow meter to predict the heat transfer rate, to adjust the maximum output power and RIMS set point and thus get fairly consistent ramp times.
