probably, and for a higher chance for happiness
I think it is something anyone moving to a country of another language should
do, but I also believe that it is right to admit those who don't - for the woman at work has done well since her move here, and if those examples you give are something people who would refuse
to learn will face, then surely that is enough to make them change their minds, if not they must be happy enough not to.
I will add, I don't know anyone who came here who doesn't want to learn English at all - it seems to be a given that learning the language will make life easier for them/create more chance of happiness in this country.