Of course they did...and no doubt took their Game dogs and Game cocks with them...as did the English,Irish,Welsh and Cornish dogmen...its a modern day romantic myth that the APBT originates from dogs that 'mostly' came from Ireland
No romantic ideas at all. It's more or less a fact that the Irish originally got their dogs from the British and the Irish bloodlines were popular with the yanks.So after the British left their dogs with the Irish the Irish just made them better.
Same as today with terrier lines (patterdales, russells etc.) , the most common breeds worked today are all of British