That's believable. England do travel in huge numbers. Must have been a few thousand in Galle in 2012 but by the time the series got to Colombo they estimated 7k England and the ground was packed. Must admit I enjoyed India in 2016 more when there was probably only a couple of thousand in Mumbai and even less in Chennai, maybe as few as 500. More authentic being away and outnumbered by home support.
As nice as Barbados is, I'm not too gutted to not be there as the island must be like one big England football away day at the moment. The Test I'd have chosen would've been the next one in Grenada, much less developed island, more chilled, and less England!