Not really, the Hive just switches the heating on and off to maintain the set air temperature in the room.
The boiler thermostat maintains the set temperature of the water circulating around the radiators (ie how hot they get to the touch when they are on) Some boiler thermostats have an 'off' position that turns the heating off completely. In the 'off' position it would stop the Hive turning the heating on.
If you haven't changed anything at the boiler end when you installed Hive and assuming it worked with the previous controls, put the wiring back as it originally was when the old thermostat was installed. What happens then if you move the black wire on the Hive backplate from 3 and put it in 1 with the brown link wire already there? If it works then, the Hive is faulty.