CDPs can be set up for specific classes only, or indeed, none at all if the CDP rate is hgiher than the regular rate. (If the CDP is expressed as base rental of £40 per day and the actual base rental is £25 or £50, you pay the £40 and don't see a % discount - but that's not how Amex works).

I've certainly seen my Amex CDP give a discount on vans, so I wouldn't generalise too much.