I'm not sure whether there'd be enough information on it so IMO it's probably best to get a letter certified by your doctor as stated in the leaflet here, just to be on the safe side.
Hopefully someone else can confirm if it's OK or not?
I had a letter from my doctor and was told I needed official proof of disability to get a DAP. I was given an EAP very grudgingly even though it clearly stated my disability (rheumatoid arthritis) and symptoms.
Everything in writing says that a letter from your doctor is enough, but some CMs are making up their own rules and are saying it's not. I've even been accused of having faked my doctor's letter once.