I didn´t chime in before because I could be accused of being biased towards writing, since I am a bit of a profilic writer rather than talker. Not that I am a good writer, he hee.
Anyway, to my thinking one skill can be of help to the other. It sounds a bit like what happens with singing, the singer that plays an instrument will be one with an edge, an advantage, since his singing will be influenced, adjusted by and complemented by the the arrangements.
It´s way easier to find the notes on a musical staff that adjust to the singer voice, etc etc.
English is a vast subject and language, so one begins by asking what he/she is going to study for? if it´s just to communicate with a friend or go to Orlando, or stay for a week - okay, no need to dig everything English. On the other hand, one might need to sit an English test, go to the University for higher studies or even use it at the office, things like that.
And that could mean a career progression, or basic requirement to certain jobs.
I myself, am a guy that just "can get by" but I would love to be good at something in English!