What is the command relationship for a NG soldier going on title 10 COADOS?

If by "invest funds" you mean if they are willing to send you to schools during a 1 year unaccompanied tour, probably not.
They got funding for a year of COADOS because the job is vacant (due to someone forward deployed or unable to fill) or they got funding for a project officer.
They will need you for the year you are there,
There might be some schooling that is job-related, especially if this is a GCC or TSOC staff job. If you have a ph 2 and/or 4 CCC reservations you will go.
However the job itself will be experience that you would not get anywhere in the Guard, and that will benefit you in the long run.

If the opportunities you're looking for are part of your job, you will get them. Otherwise, they are paying you to be there and do specific tasks. Once your year is up, if the job gets approved for another year of COADOS and they want you to stay on, that is your chance to negotiate for something you might enjoy doing that isn't exactly in line with the job. I have been told by a few of the OIC/NCOIC for these positions, "The first year is for you to learn the job and get the work done. After that, we have an obligation to give back and provide you with opportunities that aid in career progression."