I am raising a bilingual child in a non-English-speaking country, so bilingualism is something that I am fairly involved in and see all kinds of language acquisition situations every day.
Of course children don't acquire fluency in a language in six months, however generously we want to define fluency!
The ballpark figures that I have most often seen suggest that when a pre-adolescent child is immersed in a new language, it typically takes 2-3 years before their verbal abilities will be fully on track with their peers. And then another 3 or 4 years on top of that (perhaps 5-7 years, in total, then) before their academic skills will be at the same level as the other kids--IF it ever happens.
Depending on the age when children switch and the level of support they are getting, sometimes kids never really catch up and may indeed start to fall further and further behind their peers as time goes on. This is especially the case with kids who have already reached puberty by the time they are exposed to the new language.
The whole "But kids are magic sponges! They are fluent in six months!" myth comes from the casual observers of people who watch kids playing hopscotch in the playground a few months after arrival, and are like "Oh my God! She's fluent! She speaks English as well as the other kids now!!!"
No, she doesn't. The fact that she can keep up during a playground game (for example) does not mean that she would be able to (say) watch a film in English and then describe the details of the plot to you in the way that her peers would be able to. It takes a couple of years, typically, before kids are fluent in producing long, complex sentences, and building up a huge vocabulary simply takes time--there are no obvious short cuts.
Reading a complex text, like a paragraph in a history textbook, requires a very large vocabulary and fast fluent decoding (because if you read below a certain speed, you will be unable to make much sense of what you are reading). Kids do NOT acquire this kind of stuff in a few months. Especially not with English, with its horridly complicated spelling system and massive vocabulary.
EAL is complicated. It is one thing to grow up using two languages, or to start being exposed to English in, say, the early years of primary school. Kids born in the UK who are speaking Polish, Mandarin, Cantonese and Hindi as well as English from early on are actually the highest performing of all British kids.
But if we are talking about children coming to English from late primary school onwards, and if those kids are coming into classrooms in large numbers, it is going to make teaching much, much harder work.