You can fly any airplane around without trim. The C-17 has certain functions in its Flight control computer that reduce or remove the need for trim i.e. Roll Reference trim, roll automatic trim, pitch automatic trim, pitch reference trim, yaw normal mode, and EOCS.
The -1 puts it better under trim systems:
"1-1000. The trim systems provide conventional surface displacement, selection of an attitude (reference trim), or automatic trimming depending on the axis, the phase of flight, and the pilot inputs."