No, for several reasons:

1. The "expiration date" is not some hard-and-fast switch that gets thrown where what once was perfectly safe will now make you ill. Spoilage just doesn't work like that. For liability reasons the manufacturer almost certainly sets the date very conservatively, and if anything the date reflects the quality of the food rather than its safety (which is why the date is usually listed as "best before"). Stored properly, milk is likely to be safe to drink several days past its "expiration date," more if it is unopened. It will also start to taste and smell bad before it becomes really unsafe.

2. If you drink a gallon of milk, regardless of the expiration date, you will be sick; ask anyone who's been on the internet long enough to remember the "milk gallon challenge."