On the face of it, it does sound like taking the mickey but I wonder why he might deliberately do this. It is likely the two sicknesses are related but possibly sly?
If he wanted the entire month off then he couldn't have been hang-gliding in the Himalayas throughout as he went to a second visit to the GP. Do you suspect he was doing something that the sickness would prevent him from doing? Could he have been working for someone else?
Statutory holiday pay you're obliged to pay sooner or later. With any company holiday pay you'd need to follow the terms of the contract and company policy.
Could it just be a coincidence and did he notify you in good time?
Doesn't sound sly to me. My partner booked two weeks holiday for the end of july months in advance so he could be at home with the children when school closed for summer. It just so happened that he then needed an operation around this time and so the doctor signed him off for one week before his holiday and he knew then he could use his two weeks holiday to recover. It wasn't planned that was just the way things happened. Within the two weeks holiday he went for a check up with the doctor who signed him off for another week after his two week holiday as he needed more time to recover.
Its just that he was entitled to his two weeks holiday and instead of claiming 4 weeks sick pay decided to use his two weeks holiday as recovery time.
Don't always presume that when people take a holiday they are actually on a holiday/vacation.