No. Since trashing is the cost of the effect, preventing the trash prevents the effect.
Sac Construct has synergy with Crypsis and Fairie. It does not have synergy with Dues X.
Page 3 of the FAQ wrote:
Trashing as a Cost
If the cost of a paid ability requires a card to be trashed, then preventing that card from being trashed prevents the cost from being paid and the paid ability does not resolve.
Example: The Runner trashes and has an installed. If the Sacrificial Construct is used to prevent the Cortez Chip from being trashed, then the paid ability on Cortez Chip does not resolve.