It strikes me as unlikely, if people learn their accents from the people around them. If they learn their accents from television and radio, English children are as likely to develop northern accents. The farming programme early this morning interviewed a farmer from the Bristol area, who had a Liverpool accent, though not strongly Scouse, and here in central southern England I am as likely to hear northern accents as southern ones.
And then there are the mixed Caribbean/Cockney accents that have developed more recently.

There was also a report recently that American toddlers, addicted to Peppa Pig, are developing RP English accents and saying 'biscuits' instead of 'cookies'.