Time to Set-Up the Shot: If Deadshot has no action tokens and occupies hindering terrain, he can use Ranged Combat Expert and deals penetrating damage with that attack.

If Deadshot is using this power against someone using Repulsor Shield, would that character ignore the damage being penetrating?
No. Although Deadshot is using Ranged Combat Expert and the target is ignoring that power, the attack is still taking place. The damage being penetrating isn't from Ranged Combat Expert, it's from Time to Set-Up the Shot, and would not be ignored.