it doesn't mean a whole lot in the grand scheme of things. good actors will be good actors no matter the background. using a random example because the two used to be married and were in multiple films where their (excellent) acting can be directly compared: Kenneth Branagh trained at RADA and was so talented he performed a soliloquy for the Queen once as a student, Emma Thompson never trained (she studied English at Cambridge) but got her start working in many comedy series and in a West End musical.

Dead Again, starring Kenneth Branagh and Emma Thompson (also directed by him), is such a good example of this being done. Branagh plays two characters (neither of which speak with his native English accent), Thompson plays two characters, both pairs of characters exist in different time periods, the two of them were married when they made this and as a result have baller chemistry, it's good shit.