No, there's no Altman-esque borrows in this film. With Anderson's prior work that was my main criticism of his films because it is pretty blatant and unabashed. It's a welcome shift to see him have own stylizations for once.

And you're right: Altman's style is much more nonlinear and "messy" is a good word to describe it; "busy" might be another word, especially with his ensemble films.