many moving parts, but sure it has an impact.
look at some solo cup contests... the ppl that gow larger plants don't over feed, provide strong light and such... readily avialble nutes ("hydro" nutes are chelated and readily available for plant chemistry) will help greatly too. others get tiny little 5g plants for all sorts of reasons including genetics to some extent. better feed'em right with all the issues a tiny container can cause.
so, don't think "if i put it in a huge pot, i will have a huge plant" ... cause it's more complicated than that.
i'd say the biggest thing is to match the time frame to volume size... how long is it going to be in that container? is it going to get rootbound or have issues absorbing nutes etc etc... if so, the positives of why that happened better outweigh the negatives.