MV Agusta calling it a choke is a bit of misnomer, as it does no actual choking. If you watch your twist grip when you move the "choke" lever you might see it move a couple of degrees (at least mine does). If your throttle cable is not adjusted closely it will only take up the slack and not crack the throttle as it's supposed to.
Adjust your throttle cable play until you have just the slightest grip motion before the engine accelerates. This will give you the benefit of instant throttle response as opposed to slop and a delay before accelerating. Adjust both cables the same amount. You can fiddle with the adjustments until the the throttle opens as above and snaps fully shut when letting go. Don't forget to check the settings with the forks turned fully in both directions with the engine running to make sure there's no cable "pull" causing the engine to speed up. If so readjust.
That will make your choke lever very functional and when full open it will result in too fast an idle. Just have to fiddle with the whole business until you get it where you want it.