No, but Hector Allan was in Glasgow about 1800-1802 in business with Robert Tod (either his father-in-law or brother-in-law), a merchant from Irvine. Their address was the Tontine Buildings.
The family seems to have slid down the social scale following Hector's death in London in 1802. Of his 3 daughters, Marion remained unmarried, Eleanor married Thomas Doak, an Irvine joiner/cabinetmaker and Margaret married Henry David Dickie who was Secretary to the Caledonian Insurance Company of Edinburgh.
So unless your Allans came from around Irvine, I don't think it can be the same family.