Stuff like this kind of depends on your party and circumstances. If everyone is clustered, but no one is focusing the Blm, then yes. It's best to jump on that target as quickly as possible to avoid a mass sleep spell and follow up AoE damage. It leaves the healer free and clear to cast, but forcing the Dps to push harder is better than eating a party wipe.
Another thing to consider is that your actions can encourage the Dps to follow you. If you get a good burst on the Blm and drop their Hp, the Dps might try to exploit the situation. IF that happens, then be sure to throw up your Full Swing to support them. IF the Blm's Hp is dropping rapidly, then (as War) I'd probably stay on the target and try to push that extra bit of Dps to burn them down. IF their Hp doesn't drop quickly, though, then I'd swap to the healer and leave the burn to the dps.
You can usually tell where you're best needed based on how fast or slow a target's Hp is dropping (it is also a good indicator of how good or bad your Dps is at rotating their burst). IF the target's HP is dropping like a rock, then then suppressing their healer is less important because they probably won't be able to keep up anyway (unless they use something like benediction). You can toss up a stun on them if you're paranoid about it, but you shouldn't have to fully suppress them. I tend to make this judgment based on the initial burst of my Dps team. When the Dps attack, IF a HUGE chunk of Hp falls off right away then it's a safe bet they'll be able to burn the target regardless of heals. IF not, then the healer will be a problem and needs to be dealt with.
That said, IF the healer does use something like Benediction then the choice is obvious. You have to suppress the healer. Benediction's value isn't so much in a clutch save. It's real value is that it gives the healer time to keep up with the dps. It buys them time on their next cure II. After a target has been healed to full, the Dps can still burn them back down so long as Full Swing is active, but they'll need all the time you can buy them. Make sure to leave the target with a slashing damage debuff (and maybe a DoT for good measure) and then beat the living hell out of the healer for the next 15 seconds so that they fall behind on heals again. Even if they do manage to save the target, it will be at the expense of their own Hp. You'll have to trust your Dps to know what they're doing at that point.