That's basically correct -- some case endings differ only by vowel length and are therefore not distinguished in standard Latin writing, which doesn't indicate vowel length in any way. (Old Latin writing sometimes did.) "Via", in nominative case, meaning "the road" as the subject of a sentence, is written identically to "via", in ablative case, meaning "by the road", but the 'a' of the ablative case ending is longer.

However, you can't describe this as "the meter driving the grammar". The grammar requires the same cases and vowel lengths regardless of the meter you're trying to achieve. Rather, we modern-day people reading Latin poetry can use the meter to help us determine what was originally written. All of the causal influence is from grammar to meter, not the other way around.