One exception involves a band of armed men seizing a weaker population, killing off the local men, and mating with the women. Although the new leadership elite might be expected to impose it's language on the conquered population, actually the reverse occurs as the children grow up speaking their mother's language which she taught them.
What that means is you can't follow language trends to see who won.
Another exception involves immigration. Immigrants eventually adopt the language of the original population.
There's yet another more recent exception to the exceptions. DNA studies demonstrate that there's no difference between the people presently living in Iraq and those living in Iran. However, the Iranians speak an Indo-European, not Semitic, language. Apparantly a band of armed men moved in, took over, and imposed their language on the locals. This also happened in Hungary, Estonia and Finland when invading Mongols imposed an Altaic-Uralic tongue on the conquered Germanic populations.
BTW, the Nazis had a need to have all Western European people originate in the Baltics ~ it wasn't just a need to have some starting point ~ they used it as the foundation of their racial purity theories and laws ~ they killed millions of people for not having had such origins (despite the fact that no one had such origins anyway).
When it comes to written records, they are not necessarily perfect guides. Then, too, some of the written records are far older than ever suspected ~ a good example are the Sumerican records prepared by the folks who invented writing. Many of them ended up in the Bible ~ this despite the thousands of years separating them and the Book.
Concerning the "millions of Celts" just popping up, we have a couple of million people today who are descendants of two American presidents ~ John Adams and William Henry Harrison. The daughter of one married the grandson of the other and they had something like 23 children. They, each in turn, had numerous marriages, and dozens of children, and that generation then begat an even larger generation. You get "millions of Celts" after the same fashion. Just a few generations of "good livin'" and lots of sex, and there it is!