Personally, I have no experience and I don't know anyone who uses a "life jacket"
on a rod, so I really can't say.
Anytime you add weight to a rod, you are going to decrease sensitivity and alter performance. Also the larger the foam poured/slipped around the rod, the more in the way it's going to be.
The biggest thing with pouring some type of handle is that the bouyancy would have to be higher than the weight of the rod.
One solution is a tether. They make these for ball caps that clip from you to the hat. One from the rod to you is probably going to get in the way at some point.
Another solution is a Rod Rescue device built into the butt of the rod. Basically you remove the butt cap. Inside you have a spring loaded float, with an ample amount of string that is anchored inside the rod (use braid - thin for more line and strong), a butt cap with a hole and a water soluable cover. It's not going to be instant, but once your rod sinks to the bottom, the water soluable cover dissolves, the spring shoots the float out and when it surfaces, you grab the float and pull your rig back up to the boat. Not cheap to build, but insurance never is. It's hidden, out of the way, adds a small amount of weight in the butt (best place to add weight if you have to), and and gets your rig back. Main problem is keeping the cover from degrading on a rainy day and depending on what you use, you could be waiting a bit before the cover degrades enough that the float shoots out.
And yes this is real, I'm not making this up!