Is a pad spacer needed when installing disc brake pads?
The pad spacer is intended to prevent you from accidentally closing the brake without the rotor in place.  It is not required, for any part of the adjustment or installation process, as long as you do not need to bleed the brakes, and as long as you refrain from squeezing the lever without a wheel in place.

If you do need to bleed the brake, it is convenient, but not required.