yes you can sea fish with a carp rod. but you might be better off with a sea rod if its going to be a regular thing.
a sea rod tends to be thicker and stronger then a carp rod, mainly because of the current and weed. your carp rod will bounce a bit in the waves and will bend a fair bit if any weed catchs the line, but you can use it and it will catch you fish.
use your carp rod for now, 3-4oz weight and a size 2 hook, that will catch you most things. if you enjoy it and plan on going more buy the sea rod.
just make sure the sea rod is a beach caster if your fishing from the beach, 12-15ft in length and capable of casting up to 8oz's. some of the cheaper ones are only 10ft and you will struggle with distance when needed.