Does too much apple make hens tipsy?

It probably doesn't help too much but I've heard you can often stumble across wild deer which appear to be drunk because they eat the fruit which has dropped to the ground and after a period of time has started to ferment. I presume the same can happen to any animal including chickens.
As for the health effects (if any) I don't know, although my birds get fruit it is only the odd apple every so often.

A neighbour gave mine a cooking apple a few weeks ago.  They had the scoots so have asked her not give them one again. 
Jinty

Our neighbour put down her bag of apples whilst she had a chat. The little monsters were having a feast before she realised what was happening! I spend half my life apologising for their behaviour.
As to your question, fermentation depends on the natural yeasts present on the fruit (or eaten at the same time). These take time to start working - although some may be fermenting already, but this won't apply to clean good apples. In a large animal the food stays in the stomach(s) then gut for a long time giving a chance for fermentation and adsorption, whereas the residence time in hens is only a few hours. So, unlucky chooks are not likely to have a good night out on apples.  Apple cider vinegar is often recommended here and AFAIK the problem with sour crop comes when the acidity in the crop is low, so I wouldn't be too worried. Animals and insects will instinctively change foods to get a balanced diet so if they've plenty of other food they'll sort themselves out. In the wild they have to as most foods are seasonal. I'd suggest that the diarrhoea from eating fruit is mainly due to the high sugar content, helped by the high fibre levels. The potential problem here is the adsorption of nutrients such as calcium by the fibre, but I don't know to what extent this could be realised. They probably naturally make up for it by eating more grit.
I give ours plenty of apples which they seem to enjoy eating when they want to, but insist on having breakfast, lunch and dinner of pellets and an afternoon treat of corn. Go on let them enjoy.