>> Any chance of making a 2017 LT applink?
No. Maya LT has only embedded MEL script language. If someone else will decide to write it, I don't mind =)
>> So I cannot see any place in the Coat shelf within maya that will send my subdivided objects into the sculpt room. Is this not supported?
It's actually kinda of possible. Use "microvertex painting" mode for exporting your model from Maya and don't forget to set "Export Resolution" to "MID-POLY" in Options tab. In 3D-Coat import dialog set desirable subdivision for the mesh in "Display Resolution" dropbox. Do your painting/sculpting. After importing back to Maya you should have the same subdivided model as in 3d-coat.