Not any more i have not found many horses that like it over the years, I feed soaked sugar beets with chaff and electrolytes/salt or whatever after hard/sweaty work
Modern bran is not much good, it is a different product to broad bran pre 1970's. So, no, not a bran mash.
I would want to feed a sloppy mash with 25-35gms of salt, perhaps adding wet non molassed sugar beet to some conditioning mash plus wet chaff, or try Fast Fibre instead, but he should be tried on this before competition, to see if he will eat it sloppy, and to ensure the gut is used to it.
Make sure he is offered water at all times, add apple juice if he does not seem interested. Monitor his intake.
Bran mash used to be fed after hard work such as a proper day out hunting as it was considered to be easy for a tired horse to digest, times have moved on and in certain circumstances a bran mash is still suitable as something light such as after colic, in your case the horse should not be overly tired, he has plenty of time to rest and relax between classes so should continue to eat/drink normally so I can see no reason to feed anything different, I would give a bit extra if required while away but drop back once home and give him a few days off in the field to allow him to pick up any weight he has dropped.
If he has been away before and is happy on what hes on then leave it. No good in changing it whilst away from home in case of possible side effects. Bran nowadays is so dusty in my opinion and unless soaked properly doesn't suit my horses very well.
I still feed bran mash after hunting! Not because it is easy to digest as suggested above but because it is hot (well warm anyway!) highly palatable and it gets the gut contents moving reducing the risk of colic. Horses out hunting can go for hours in a high energy situation without much food or water. They then box home often stuffing their necks on hay. A bran mash makes sure they don't block themselves up! However it has no real nutritional value - it is a low energy bulking agent. The horses get a proper feed a couple of hours later when they have settled.
I also compete SJrs in multi day shows - and no. I wouldn't feed bran mash in that environment - unless I had a reason to suspect that a horse might be a bit colicky for some reason. I do feed elecrtolytes, especially in the heat, soak hay and feed wet feeds - just to make sure they can get enough fluids. Best thing for long shows is - as others have said - not to change anything!