Work experience can be very hit and miss. they will only offer you any if they have the time and inclination to do so. Asking closer to the time decreases you chance of getting any.
Only being available for a short time period also makes it less likely.
Most finding out about them and a poor application also make it less likely. The better your application, then the better your chances of making a good impression.
The more likely is if you know someone/ manager who works there. Normally letting anyone on the premises has to be cleared through HR and that takes weeks. Dont be surprised if they say no, but you have nothing to lose.