Yeah, the Solex 4A1 Carburettor is the stock 280 unit, rated at around 430cfm as far as I can tell.
The carburettored 2.8 returned 115kw (154bhp)stock, compared to the K-jetronic engine ratings of 130 and 135kw (175 and 182bhp depending on your model).
It makes sense to me you're more likely to find AMG tuning options on the 280E/CE variants, but then I don't know if AMG offered a 280C option. Maybe they did, but maybe it was just the body kit.
I should think an engine tune on a carburettored 2.8 would bin the carby for something a little more performance orientated or even a sidedraught setup fairly early on.
If someone sold you a 280 "CE" with a solex carbie on it, I hate to break it to you but it may have been a 230 or 250C (or whatever the lower capacity engines are in the W123 coupe) someone's gone and transplanted a 280 carburettor motor they bought cheap. Then changed the badges to 280CE but never got around to fitting the K-jetronic. The lower capacity models are also more likely to have a manual transmission than the "luxury" 280 models.
Check your compliance plates to see if the engine is original.
Either that or the "CE" badging may have just gone on it at the same time as the body kit (I knew this guy who kept putting a "supercharged" variant badge on his naturally aspirated, local Calais model every time he had to get some bodywork done, he just liked the badging I guess).