Any idea on whether the diving will be any good two weeks after a large storm like this?
I can't comment on the infrastructure, but based on the few articles I have read, I think it's reasonable to assume that most places will be open for business, although perhaps with a few twists. This is the kind of event where "friends" trumps "competitors" and you may find a boat from a shop with a missing dock, using the dock of the shop next door. As others have said, more than anything, what the people of Belize need right now is money, so either donate the value of your trip or go! (Which is way more fun, and maybe you can even pitch in to help clean up while you're there.)
From a purely diving perspective, I can share this: Several years ago, we arrived in Turks and Caicos literally 3 days after Hurricane Irene smacked that country down. If I recall correctly, Irene was a category 3 storm. We were doing a week on the T+C Explorer.
When we jumped into the water for our first dive, what was laid out before us looked like a post-war apocalypse. The visibility was about 25 - 30 feet. Everything was literally covered in sand... the corals, sponges... everything. There didn't appear to be many fish. We were used to seeing sharks on every dive in T+C and there were none. (We had been there the previous summer as well, so we knew what they could be like.) To say we were disappointed wouldn't come close. Not only because we had dropped a ton of money for what was apparently going to be a week of crappy diving, but we were almost heartbroken over the state of the reef.
When we sat down for lunch that first day, the talk was all about the state of the reef and visibility. Our Captain commented that T+C is known for it's beautiful, fine, white sand beaches. And of course the downside of that fine sand, is that in a big storm, it's easily picked up and "dissolved" into the water column. He also commented that this wasn't the first hurricane in history to hit these islands, and the reefs had always bounced back. He matter-of-factly said that the next "blow" would clean everything off again. Of course we didn't care about the "next blow". We cared about "this afternoon".
By the next morning, things had improved significantly. Vis was much better, but far from awesome. There was still tons of sand on everything, and it looked horrible. We spent a lot of time "fanning" sand off of corals and sponges with our hands (That probably didn't help the vis any!). I resolved to shoot macro all week.
On our third day (we had moved far away from Provo by now) the visibility was probably approaching 100', but the water was still "hazy" for lack of a better word. Lots of fish were foraging and we were seeing bigger stuff. We realized that these critters would have instinctively headed for deeper water during the storm.
And so it continued. By week's end, vis was fantastic and critters were plentiful. There was still lots of sand on stuff, but it was much much better than the early part of the week.
I haven't been diving in Ambergris for 20 years or more, but I spend a lot of time in the outer cayes. My overall impression of the sand is that it's very coarse and a lot of it is crumbled shells and stuff... not really the kind of stuff that stays in solution very well.
I suspect that if you arrive in Belize two weeks or more from now, the visibility will be fine, the fish will be plentiful and things will be pretty much normal. Undoubtedly, there will be some broken gorgonia and sponges, but that's life on the reef.
It may not be perfect, but it will still be amazing and you'll be helping our Belizian friends get there lives back to normal that much sooner.
This is one of images I shot that week... A porcupine puffer... hiding from the fallout! As you can see, he's still smiling. ;-)