Yes it will work but you should connect a C wire.
Do you see a extra wire in the wall not being used preferably blue color?
You would use extra wire to C and then at the system terminal strip connect to C there also.
It looks like your system has 2 stages of heating and cooling so connect the wires to same terminals as on the nest.
Thank you for the help, @Houptee.
@Mturetzky, I'd be happy to take a look into this for you as well. Since you have 2nd stages of heating and cooling, it's only compatible with a Nest Learning Thermostat 3rd gen. Like what Houptee said, you can follow the same wiring configurations and a C wire or a Nest Power Connector may be required to deliver constant power and stabilize the flow of current into the thermostat.
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