So I'm looking for further inspiration for an Alesha, Who Smiles at Death commander deck. I was wondering if Boast abilities could be activated when the creature comes in tapped and attacking. I know that it skips over triggers that would only trigger when a creature is declared as an attacker. However, Boast looks different to me since it looks like an activated ability that works as long as the creature attacked that turn.
No, it doesn't work, for the same principle that "whenever this attacks" triggers don't work.
A creature that is put on the battlefield attacking is attacking, but it never attacked. You can't activate Boast abilities of creatures Alesha put on the battlefield.
If a creature with a boast ability is put onto the battlefield attacking, it was never declared as an attacker. Its boast ability can't be activated that turn.
No. For the purposes of the activation instruction on boast abilities ("Activate only if this creature attacked this turn and only once each turn" [C.R. 702.142a]), a creature that enters the battlefield attacking hasn't "attacked" this way, any more than it has "attacked" this way for the purposes of triggered abilities (see also C.R. 508.4).
EDIT (Apr. 30, 2021): Edited to conform to update with Strixhaven.
Anyway, say I bring back Varragoth, Bloodsky Sire with Alesha, Who Smiles at Death tapped and attacking. Can I activate Varragoth's Boast ability?
Yeah, that's my fault...
A creature that is put on the battlefield attacking is attacking, but it never attacked. You can't activate Boast abilities of creatures Alesha put on the battlefield.
Reference: Kaldheim release notes
If a creature with a boast ability is put onto the battlefield attacking, it was never declared as an attacker. Its boast ability can't be activated that turn.
EDIT (Apr. 30, 2021): Edited to conform to update with Strixhaven.
Yeah, that's my fault...