powers – Do quick objects to grab and move (damage) work together?

The damaging modifier on the Move an object Power (page 119) states:

Damage: Your effect can deal damage, such as a Normal Force application with damage equal to its rank. This includes targets that can be injured in seizure and remote attacks.

The text would imply that Move Object is able to "grab" a target:

This includes damaging targets to win

In addition, the DCA version of the Hero Handbook contains six examples of moving objects used to move and grab people, the Wonder Woman's Lasso of Truth being the most important.

the Fast entry Advantage (page 84) indicates:

When you hit with an unarmed attack, you can immediately perform an immediate check against that opponent as a free action (see Capture, page 196). Your unarmed attack deals its normal damage and counts as initial attack check required to seize your opponent.

The question is:

Is a remote telekinetic version of an unarmed strike considered an unarmed strike for the purpose of quick entry?

And would it be different to use Fast Grab during a close attack that required a real unarmed strike?