This is a trick I learned crewing for a fellow in Florida who always stored not one, but two, rope anchor rodes on his foredeck while cruising. He even kept them there on offshore passages, lashing the coils of rode to stanchion post bases, and never had a problem. The big advantage of doing this, if you have a boat with a belowdecks rode locker rather than a modern anchor well, is that it saves you the bother of pulling all the rope down the hawsehole.
If you’re cruising somewhere with lots of mud on the bottom, storing your rode on deck also keeps all the mud that clings to it out of the interior of the boat. Unlike a chain rode, which can be easily rinsed off as it comes aboard, a rope rode tends to want to stay attached to its mud, at least as long as it is wet. Much of the mud will fall off after it dries and turns to dirt, and if the rode stays on deck, the dirt will too.
When I was cruising on Crazy Horse, my Alberg 35 yawl, which I always anchored on rope, I often kept my rode on deck when cruising up and down muddy rivers and creeks. Like my old skipper, I just kept it in coils on the foredeck, although some people may prefer to store it in a bucket or a bag.