When the acute accent stands over a vowel, does that vowel become long automatically?

e.g. βάλλομεν - is the βάλ Syllable long?

No, acute doesn't make a vowel long (recall e.g. φύγετε). In βάλλομεν the vowel is long not because of the acute, but because two consonants (λλ) follow it.

βάλλομεν. There is only one accent for the modern Greek language.
The placing of the accent is to show where the stress is put on the syllable. The length of the vowel remains the same. In this word for instance the ' ά ' is prounounced like the 'a' in the english word 'Pal'

We are talking about ancient Greek. But, there is not only one accent even in modern Greek. Aren't Cavafy or Elytis modern Greek poets? They don't use just one accent. And they are not alone on that.

How modern Greek should be written can not be decided by a government; it is decided by those who write in that language. At the moment, most of the important modern Greek intellectuals, poets, researchers, etc. write in polytonic Greek.