From a UK perspective, there is very little call for Divers qualified as civil engineers on a marine civils job. I know of a few, but they worked for an Engineering and design company which occasionally required one of their engineers to get in the water to inspect the works done. It was normally cheaper for them to have a couple of their engineers to be in-date divers than to employ a 3rd party diving company to inspect work, especially if viz was poor. Others worked for a company which had a bridge inspection contract, where most of the inspection was above water, some of it just wading around in a suit, and the occasional dive had to be done for deeper work.
I think a background knowledge in engineering doesn't harm anyone who wants to be a better diver, but a degree would be overkill, and a lot of work and time also.
It's unlikely you would be able to 'fall back' on one or the other of those careers also. Diving, like Civil engineering, requires many years of dedication before you get 'good' at it, and become connected and employable. I can't see many guys succeeding in both careers, when so many cant get work in one of them just now.
I think you should sit down and have a long think about which job you want to put your effort into. Diving has been great to me, but from experience, I'm an exception. Out of 14 guys who trained in 1993, only me and two others were working a year later, and just after that one of them was killed in a diving incident, the other got out of the industry leaving just me by year 2...
You can travel the world working, still, but it isn't like it used to be. Foreign countries are getting wise to importing their expertise, and are pushing for local people to train up to take your job, and rates can be ridiculous (about 10 years I was working in the gulf of suez for $700 a day, and the local divers were on $50. It's not hard to see that it is considerably cheaper to throw a lot of cheap guys at a job hoping one can do it at those margins.
There's no job security, engineers are constantly trying to 'engineer-out' manned intervention on most designs, and even if you are the most cautious diver, your life is still in the hands of dozens of other people, most you will never see.
Civil engineers either travel from contract to contract or basically have an office job, the money seems to be ok, but every site I've been on, as the workers leave, the light is still on in the engineers hut, and they always have that 'heart-attack at 40' kinda look....but I'm not a civil engineer, so I'll leave that job description to an Engineer!