Do the four engines make the BAe efficient? No! Does it affect performance? Yes, very much so. The BAe 146 occupied a niche for Hot & High airfields, in that it can continue the takeoff when an engine fails: one failed engine out of four leaves 75% of full thrust.
But 4-engined planes have worse fuel economy than an identical sized twin engine, due to decreased efficiency of a smaller turbine, and increased drag from more engine pods and a larger vertical tail area. That, plus the overly stubby 6-abreast size fuselage, made for much worse fuel economy than a comparable size aircraft like the Fokker 100.
Not an aerodynamic performance parameter but definitely a cost performance one: maintenance cost of four engines is twice as high as for two engines..