Probably. KitKat is lighter on resource so any phone that can run JB ought to be capable of running KitKat.
When you get it depends on your phone and - if you bought a network subsidised phone - your network.
The way it works is Google release a new version of the OS (e.g. KitKat). If you have a (recent) Nexus device (or one of the Vanilla version of non-Google phones), you get an upgrade OTA (over the air) within a few weeks (just got mine for my Nexus 4).
If you don't have a Nexus, the manufacturer has to add their customisations to the new version of the OS. That takes time and if the phone isn't a current big seller, there's a good chance the manufacturer won't bother. If they do bother and you bought SIM-free, you get your upgrade then, either OTA or via a PC tool depending on the manufacturer.
If you didn't buy SIM-free but got a network-subsidised phone, once the manufacturer had done their thing, the network also has to do theirs. This will take a further period of time. Usually, quite a long time. Again, not all networks will bother to do this for all phones. If they do, you should eventually get the upgrade OTA or via a PC tool.
The alternative is to root your phone and install the new version yourself. Note that rooting may affect your warranty. For more information, see the Rooting section of your phone's sub-forum.
