How to align the text at the path point?

Daniel,

You may:

1) Tick Use Preview Bounds in Edit>Preferences>General;

2) Select the live Type with the (normal) Selection Tool and Effect>Path>Outline Object.

That will give you a Bounding Box that fits tightly round the live Type, and will ensure centring (both directions) and keeps doing so when you edit.

But if you need it as non outlined text in PDF you will have to remove the effect:

3) With the live Type selected, in the Appearance palette click the Reduce to Basic Appearance button.

That will bring it back to normal plain Type.

Obviously, you will need to untick Use Preview Bounds for other purposes, but you can just tick that again when you need to edit (some of) the Type if needed to keep it in place; that may not be necessary because the changes will (mostly, and only if no letters exceed the hitherto vertical bounds) be in the horizontal direction.

i think the bounding box is probably defined by the type metrics/em square with live type, so i don't think you can just constrain it to the visible characters without outlining.