In my experience, about half of the benefit of learning a new language is in better understanding of grammatical structures (eg. cases - English has them too; and tangentially, (foreign) language classes taught me more about English from a grammatical perspective than public school English classes), and about half of it is seeing how languages relate to one another (eg. how so many words and phrases in English - and other languages - are derived from Latin). You could get the former, but I doubt you could get (the same level of) the latter from another language.
Now of course that's vastly simplified and I'm sure there are other mental affects (and numerous benefits to learning live languages), but those are the ones I've noticed, and the effects would definitely be different.
Now of course that's vastly simplified and I'm sure there are other mental affects (and numerous benefits to learning live languages), but those are the ones I've noticed, and the effects would definitely be different.