gmaker0507:
Is it possible to test it out w/o soldering? Can I plug it into my breadboard?
No, because you have to assemble the display to the driver board by soldering and you have to assemble the four pin header to the board in order to plug it into the breadboard.
Adafruit:
A bit of soldering is required to attach the matrix onto the backpack but its very easy to do and only takes about 5 minutes.
Not too infrequently, fellows come here having tremendous difficulties and after much back-and-forth questioning, it turns out they have just sat the parts together without soldering.
gmaker0507:
I noticed this similar display is shown in the preview pictures being straight attached to a breadboard.
Indeed. Because the display itself has pins on it which can either be soldered into a PCB or pushed into a breadboard.