I always had the impression, that grenades are basically treated similar to melee weapons in the assault phase. Just that they only have one attack. Similar to melterbombs (which are classified as grenades but can't be thrown ...).
While the theory they could probably be thrown during overwatch, normally grenades are blast weapons and therefore can't be fired/thrown due to only snapshots allowed?
But I can be wrong on one or all things stated, I always forget about grenades so don't really know the rules for them that good