Ok, so I have this same boiler that I wanted to add a Nest to and I spent a little time looking into the wiring of the boiler a little more carefully.

I am slightly afraid that the Nest can bypass the pressure switch and low water cutoff if wired to the T-T terminals directly.  I had an issue where the Rh wire was connected to the BROWN T wire coming off the pressure switch and the W1 wire connected to the ORANGE T wire.  When the pressure switch cut off the power (as it is supposed to), the Nest complained that there is was no power going to Rh.  For some reason when this happened, our furnace kicked on and stayed on, which if you look at the wiring diagram shouldn't happen.  It seemed as if the Nest supplied power to the W1 wire from its battery - essentially bypassing the pressure switch and low water cutoff - which could be scary.

I think the best solution for a Utica or similar boiler with a (T-T) connection would be to purchase a simple 24VAC relay (http://a.co/d/2RS0NHC).  Connect Rh to the load of the 24V transformer (you can use tap into the same transformer that is on the side of the furnace), C to the common (NEC) on the transformer, & W1 to the relay control coil pole (1 on the linked relay) and then back from the other relay control pole (3) to the common (NEC).  Then hook up the T terminals to each side of a the normally open poles (2&4).

This way the nest will essentially work like a dummy switch and you don't have to worry if it does anything weird.  It will always have power and won't bypass any of the essential cut off functions of the boiler.

Edit:  Found this little video on Youtube which pretty much explains exactly what I described here.  It's not a Utica boiler, but it has basically the same type of T-T terminals for a thermostat and describes how to install an isolation relay for a smart thermostat. - https://youtu.be/f0v3FeDZBeY