[nikanj]

Nope, the ”trust this computer” dialog needs you to enter your passcode before any other actions are possible

[yangm97]

This can be bypassed by putting the phone in DFU mode.

[cedws]

Probably the only hope is jailbreaking.

[sheiyei]

Jailbreaking a locked, inaccessible iphone?

[userbinator]

Keep in mind that everyone else is usually unaware (by design) of what all the intelligence agencies can do, but I doubt they would help in this scenario even if they could.

On the other hand, if this happens to a far more important person...

[cachius]

Jailbreaking is dead.