From what I can gather after reading through several different sites in a search, it will depend somewhat on the type of alcohol (I am assuming schnapps) and the method used to turn it into alcohol.
Archer appears to make liqueur type schnapps, which means that the fruit is steeped in the alcohol base, rather than distilled from the fruit itself. This means it will have a higher sugar content, and will go bad faster.
As near as I can tell, there isn't any adverse health effects reported from drinking out of date alcohol, but the taste can vary wildly, and be anything from a "flat" taste, to very harsh and bitter as the sugars continue to break down. This is moderated by temperature and how much air is in the bottle.
So there shouldn't be any health effects, other than possibly bad taste.