yeah that looks like it, pic is a bit blurry
is the hole though the middle open ?
push a piece if wire through it to make sure, wiggle it around etc then blow it out
is the any holes that go across the jet in the smooth/threadless area ?
if there is, check that they are clean/clear too
then look into the carby where that silver Pilot jet screws into,
at the bottom of the hole there is a tiny hole that goes through to the main bore of the carby
that needs to be open/unblocked too
use an led torch or similar to look down inside it and check it look clean
blow it out with compressed air and reassemble it
once you have fitted it back onto the bike, start it up.
then turn the idle speed screw inwards to raise the idle speed a bit, about 1800 rpm, not too high
now the mixture screw, towards the air filter end of the carby, can be adjusted.
turn the screw out a quarter of a turn.
listen to the engine carefully,
if the rpms drop, then the mixture screw needs to be turned in a 1/4 of a turn.
the rpms should increase to what they were,
now try tuning the mixture screw another 1/4 of a turn in
if the rpms increase again, then try another 1/4 of a turn in.
if at any stage the rpms drop, or it starts running funny, then turn the mixture screw back out a 1/4 of a turn
adjust the mixture screw, until the engine is revving at it's highest/smoothest point
when you are happy it is close to perfect, then you can unscrew the idle speed screw (with the big spring) until the rpms drop back down to a decent idle speed.
now you can take the bike for a ride and see how it runs
listen and feel how the engine is running, if it hesitates or feels flat etc, take note when it happens, and at what throttle setting
eg splutters at 3/4 throttle
then come back and post up you findings
we can go from there.