nope, you won't necessarily need the intonation tool to intonate your guitar.
to cut short:
tune your guitar and check each string tuning at 24th fret. if the note is sharp, detune the string slack, with the allen key loosen the screw that fastens the saddle to the trem base-plate and move the saddle a bit backward. then tighten the screw, retune the string and check its tuning at 24th fret.
viceversa, if the note is flat, move the saddle a bit forward.
repeat for each string.
of course, you have to adjust intonation just when your trem is set parallel to the top of the guitar, or perpendicular to the trem posts.