Does this card's [Your Turn] effect trigger when this card is in the breeding area and would digivolve into a Digimon card with the [Demon] or [Titan] trait?

A Digimon with this card in its digivolution cards attacks, and another effect trashes a card from my hand. At such times, if I activate this card's inherited effect and perform a digivolution into P-209 [Titamon], can I then activate P-209 [Titamon]'s <Alliance>?