That is not conversely true.
There are languages which are non recursively enumerable, unresrticyed grammer can be defined in any form or format to even specify those languages,
Consider this, if there is a non RE language, there will exist a grammer for it (by the definition of languages) but it cannot be claimed that language generated by a grammer is RE or non RE.
Its a membership problem for RE which is undecidable.