Wearing race number under wetsuit

I've seen it, but i would definitely try it in training first.  All kind of things get caught up/tangled in the suit, especially when you're wet.  A race belt is so easy to put on later.

I would also be curious to see your routine.  Put everything on the bike that you want to take with you, such as sunglasses, nutrition, fluids, shoes.  That should all be tucked away and ready to go.  The only thing you should be putting on after the swim is helmet (and apparently race belt, that is a bummer)..  EVERYTHING else happens while you're riding.   Your wetsuit should be at your waist or totally off, goggles and cap in hand, by the time your reach  your bike.  

Have you ever watched an ITU triathlon on TV?  They focus on the pros and you can see how they transition. It's super fast.  You could possibly find this on YouTube.

ETA: Same advice for T2.  Take off helmet and put on shoes, but everything else happens while running (I put on my visor, racebelt and maybe tuck a gel in my pocket.)  T2 shouldn't take more than 10 secs longer than the amount of time it takes you to traverse the distance from bike in, your spot, run out.

^^^This^^^  Don't use a towel in transition for anything other than sitting your things on, and wiping your feet before putting on socks (assuming you're not going sockless, and doing flying mounts & dismounts from the bike.  Fast transitions require keeping things as simple as possible.  Nothing extra.

Here's a picture of what a good set up looks like for someone wearing socks.  For the guy who said he struggles with getting socks on, notice that they're rolled up and stuck in the bike shoes, so all you need to do is slip your toes into them, and unroll them onto your feet.

Answering the OP, practice it in training, but you should be fine wearing your race belt and number under your wetsuit.  I've done it personally, and have had athletes who've done it without any issues.

 ETA: By the way, if you're doing a race like most, that doesn't require your race number on the bike, clip your race belt through the back strap on your running hat, and put both the hat and belt on as you're running out of transition.  Don't take the time to do it at your transition spot.

I've worn my race belt under my wetsuit for years and have never had a problem.

The race number is facing forward on your stomach and flipped up as you pull up the wetsuit.

Unless you have to have the race number on your back on the bike, I'd leave it facing forward.  

Some race bibs can disintegrate in the water - I've read that in a few of the "fine print" sections of race packets. 

I usually grab my race belt and put it on as I'm running out of transition. It's not a difficult multitask.

zed - 4 minutes is a lifetime in a sprint race.....you've got bigger fish to fry.  Practice putting your belt on and were to have it in transition for the fastest application, and move on.

Unless there is a long run in/run out there is no reason you shouldn't be closer to two minutes in transition.  How often do you practice your transitions?  Very overlooked aspect.  One of the local tri clubs here sets up a few racks by the lake several times a year and folks repeat coming out of the water and onto their bikes.  Time well spent. 

I done both - worn it under my wetsuit and put it on transition. 

When i did wear it under it was that plastic kind of material bib and it was on a race belt and wore it in front during the swim. Swims here are 99% of the time wetsuit legal so i wore one. I honestly didn't notice it and it was completely fine. Now i am not competitive, i just forget stuff in transition so it was one less thing to forget. But it's not something I need to do or i don't think it actually saves all that much time over hanging it on my bike bars and remembering to put it on in T1. I still wear socks on the bike ...