Because a WiFi connected thermostat is always using power, it may need the C or common wire from the source (in your case, the boiler). Now, depending on the configuration, it MIGHT work without that wire, but it certainly will work if you can provide it. Some simpler digital thermostats rely on just replaceable batteries. The Nest does have an internal, rechargeable battery. Keep in mind a simple thermostat is basically a light switch. When needed, it closes a switch to apply power to something to make it work. But, the switch itself doesn't have a 'return' to complete a circuit, that return is in the boiler or furnace. On a HVAC system, that 'return' is the C connection. The thermostats like the Nest prefer constant power. THey can work with some systems without it, but you can't really tell for sure until you try it, then need to run another wire, if it isn't already in your cable. If there's a spare wire in your cable, or you can run a new one, it's certain that it will work.
Different systems work best when the thermostat is properly setup to complement it. The better digital ones have multiple setups. Some of them, including the Nest, 'learn' the response of your heating/cooling system, and instead of just being a dumb timer, can adjust when it needs to start to get the temperature where and when you want it. But, in setup, you tell it the kind of system, whether that's forced air, hydronic, etc. I know at least some of the Honeywell ones can do that as well. There are certainly some others, too.
I've had a Nest thermostat installed now for about 3-4 years. FWIW, Nest was bought by Google, and if you want to use some home automation that is based on Amazon's entry, you may not get full integration with your thermostat.
