The answer is no, they will not -- and you must remove the battery immediately and dispose of it safely.  If you do not, the battery will destroy the system in short order.  
Hi all My 3 year/4 month old Alienware 15 R4 battery has swollen up suddenly, its split the palmrest and is raised up. Warranty ran out April 2020.   Will Dell still cover this? In my opinion this shouldn't happen regardless of being out of warranty. I have an old Acer that is 10 years old and battery hasn't swollen. Please advise, UK based.  Thanks
15 R4, battery swollen, split palmrest