I'm still not 100% clear on the end result you are after.
However you can move Type on a Path in two ways.....
Baseline Shift on the Character Panel.
Type > Type On a Path > Type on a Path Options and set the
Align to Path to center.
How you cover up or hide the path behind the type is another matter entirely, if that is indeed what you are trying to do. -- You could add a white stroke to your type on a path and move it behind the the
<characters> item in the Appearance Panel.
If you actually want to join the type to the path under it, then you'll need to outline the text and cut/join anchors to make multiple paths into a single path. Basically, there's no "two button click" solution to what you may be asking. You'll have to edit individual paths or the text to create the appearance you want.