I need some help regarding my dead PS4 Pad

This is the situation: My PS4 pad died randomly despite the fact that I only used it like 3 times (Im a PC gamer kinda guy).

The pad wont charge, wont turn on, nothing.

I read on the Internet that if Imget this dock that charges from the bottom, the joystick will work.

My question is: If I buy this, can I sync the control with the ps4 even without the usb cable? This is the only pad I habe and I dont want to buy another one anytime soon.

Thanks in advance guys.