Hello Amy - I don't know of a connection between the Pattersons you mention, and my great-grandfather, but that doesn't mean there isn't one. It is likely a distant one if it exists as I don't believe any of the Pattersons I'm looking for emigrated.
All I know about Thomas Patterson is that he was born about 1859, and married Isabella Bowman of Killinchy in November 1878. Their first child was born in Larne, which I thought might provide a clue, but no luck. Their next 2 children were born in Ballyministragh (near Killinchy, where the Bowman family lived), then the remainder were all born in Belfast. Thomas Patterson was a baker, and died of typhoid in 1899. His widow and children (ages 20 to 1) were listed at 40 Witham St in 1901 census. In 1905 they all emigrated to Rockford, Iowa.
I agree, Patterson name is difficult to trace. By searching Belfast City Cemetery records, I was able to find a record of Thomasina Patterson buried at Knock, which I can link with Thomas/Isabella Patterson's family. The death notice for Thomas Patterson indicates he was to buried at Knock, but I can't find a record for him through the 'search'. I'm hoping to find Thomas and Isabella's marriage record at PRONI in August, which might provide Thomas' father's name.
Short answer = I don't know, but not very likely :(