OK, let's say you're trying to track the 270 radial inbound (i.e., fly a 090 course to the VOR). You are located west of the VOR and north of the 270 radial, headed 090, so the needle is deflected fully south (i.e., to the right on the CDI). The system will command a standard rate turn to the right, and will continue to command that turn as long as the needle remains pegged right. If the plane is located more than 10 degrees north of the 270 radial, the needle will never come off the peg, and the airplane will just continue making 360's to the right.
If the plane is closer to the radial, so it crosses the radial in the turn, the airplane will begin rolling out of the turn as the needle centers. In the case you describe, where the plane reaches the radial on a southerly heading just as the needle centers, the plane will roll wings-level as the needle centers, but on a perpendicular heading. As the plane continues south of the radial, and the needle begins to swing north (left), it will begin turning left slowly, and increasing the turn rate as the needle deviates further to the north (left). You'll end up S-turning across the radial, possibly in an undamped oscillation which will never stabilize on the radial.
All that is why the C-I manual says not to engage the track mode until the needle is within one dot of center and the heading within 10 degrees of the desired course. If you start that close to "on course", the unit is close enough to "in sync" that it will result in damped bracketing to a good tracking solution.