Is there a Tasha costume for Online Mode?
Yes. A Tasha Costume Set for the player avatar is part of the Deluxe customizable cosmetic set.
Confirmed explanation
The costume is an online-avatar cosmetic and does not make Tasha herself a playable pilot or Deluxe-exclusive campaign character. It is listed separately from aircraft skins and missile smoke.
What is not confirmed yet
Individual costume pieces, alternate colors and later sale availability are unconfirmed.