Carronades, no. Flaks maybe. The carro (as far as I'm aware) doesn't do AOE damage. It's essentially a cluster of pellets fired from the gun in a cone shape. Each pellet is a direct shot with no added AOE damage. The burst round will just increase the ammo on the small carronade and reduce the fire rate. Not really worth it. On the heavy carronade it just slows down the rate of fire, absolutely not worth it.
The flaks do AOE damage (after the arming time), so burst rounds can be effective on them. Letting a single shot hit more components at a time. I'm not 100% on how AOE damage works, but I believe that it applies damage to each component in the AOE zone equally; and doesn't hit components more than once. For instance the hull has lots of hit boxes (you can see the hit markers appear in different areas) but an AOE shot will just hit it once (where the various 'pellets' from the carronades will each hit it).
It will increase the ammo on the light flak along with the larger aoe, and slow down the firing rate. The light flak already fires pretty slow, so this can be a little bit of a bother. On the heavy flak, it will fire slower and not effect the damage, on top of the increased AOE. The AOE on the heavy flak is pretty large, and with burst rounds it can get quite impressive.
Essentially it's usually a good choice for flaks, but never for carronades.