My back molar is decayed i've had pain for 3 days now and my cheek is super inflamed . would they do an extraction ?

Maybe: You would really need to see a dentist to get an evaluation of the tooth and possible x-rays to see the extent of the infection and whether you would need antibiotics etc as well as a possible extraction. Good luck.

Yes if healthy: There is no clinical reason not to take out an infected tooth from a healthy person. Assuming there are no systemic problems, heart disease, immunological diseases, the extraction would probably be done.