Noisy and chaotic does not a comedy make This film is a celebration of the Greek family and it is successful in doing this. But while watching a large family, full of quirky characters, with noisy and chaotic interactions, can be enjoyable, amusing, and even funny at times, it does not, in itself, make for much of a comedy.
The main problem is a lack of dramatic tension. There is a small amount in the transformation of Toula from restaurant drudge to attractive travel agent, which did involve a funny scene, but that piece of comedy was soon over. Toula and Ian got on well from the beginning. This is more natural and original than the standard romantic comedy, where girl meets boy, they either hate each other at first sight or for some other reason can't be together, and at the very end they manage to get together after all. This is completely unoriginal, but, and I cringe to write this, it does create some dramatic tension which can let the comedy work.
Ian is always accepting of Toula's Greek heritage, so there is only a small amount of humour in his being an outsider. By the time Toula's father finds out about Ian, the couple's relationship is solid, so there is minimal opportunity for conflict and the development of comedy. There is some comedy in the contrast between Toula's and Ian's families, but his parents are peripheral to the story, so the amount of humour that could be generated was minor.
The film is a portrayal of a large, close-knit, family, for the audience to enjoy and laugh at. But there is limited humour in the plot, or even the two main characters, and so ultimately it is limited in its success as a comedy.