That happens quite quickly when you mix people with differnet accents together. People keep their accents if they are around other people who speak like them, so for instance irish people maintain and irish accent in ireland.
I worked for the British army in berlin for a while and I noticed all the young soldiers had the same accent, which was a mixed working class British accent, and you could not tell where it was form, because it was so mixed.
The same would have happende in the US, as all the immigrants mixed their accents, and began to speak the same way in regions of the country where they lived togeather for a while
So it only takes a few years.