Personally, I don't think it's wise to consider it as you're talking about risk of infecting an open wound, even in your drysuit this is full of nasties unless you Milton it before diving...
Combine this with the hyperbaric effects of breathing compressed gas at depth and you're into the realms of seeking advice from a hyperbaric specialist
Hyperbaric oxygen therapy is used for burn treatment, which may be why finbar's burn healed quickly.
But common sense suggests you either need to stay dry and enjoy the sun, or if you're desperate not to skip the dives then get professional advice regarding the state of the burn, and possibly also from the chamber people about what risks you're running for the deep tissue healing and DCS issues.
Spike Milligan's SCUBA rules:
"If you never have a plan, nothing can ever go wrong"