I would say no. While it says attack, it seems to me that the intent is to allow you to re-roll weapon damage, not additional damage. This is from the Sage Advice, which says that Sneak Attack is not weapon damage.
"Does the benefit of the Savage Attacker feat apply to additional effects like the rogue’s Sneak Attack or the paladin’s Divine Smite? No. The benefit of Savage Attacker applies only to rolls of the weapon’s damage dice, not to any extra damage that a feature or other ability might grant."
That would be my interpretation of the rules. As a DM, I wouldn't have an issue with it and would allow it anway.