The dolphin system is not complex enough. We know this because their brains are not as complex as ours. If we relied on a system comparable to theirs, we'd be failing to communicate a huge amount of what we are capable of thinking.
The question isn't really 'how complex is the dolphin communication system?'; but rather 'how complex is it capable of being, with a different brain in control?' That they haven't produced a system of complex grammar like ours doesn't mean they can't make enough noises to do so.
Perhaps a better example is birds. Some birds can produce a much greater variety of noises than ours, and they do so without the oral apparatus of humans. We could make do with a fairly simple hole - no teeth or tongue necessary. What we'd need is some sort of internal apparatus similar to a bird's syrinx. It wouldn't need to be as complex as the most complex amongst birds, since we don't need to be able to make noises like a lyrebird for human communication. We'd need to make the anatomy somewhere in the trachea a bit more complicated, but in exchange you wouldn't need the complex anatomy that we currently have around the junction of trachea and oesophagus, and choking on food wouldn't be an issue.