Basically, yes. It's odd that it would say it has no uv coordinates though. Did it say it had coordinates out of bounds or just none at all? Either way, if you create a new uv map for the subdivided mesh then you can't use the generated texture map on anything but that mesh that's in the uvmapper. If you try applying the resulting texture to the old mesh then it wouldn't match even when subdivided.
So your three options are:
1. Convert the original mesh to subdivided, then convert to mesh to make it permanently subdivided. Then export it to .obj, re-uvmap it, re-import it, and then apply the texture map to it. You result in having a high poly model but you don't have to worry about warping.
2. Just keep the original mesh and convert it to subdivided, then try to repaint it to compensate for the warping.
3. Follow my steps which results in just the high poly texture map but the mesh isn't re-uvmapped, and use it to aid you in repainting it to compensate for the warping.
The warping that occurs when unwrapping subdivision-based models is why you try to keep certain areas separate. Like model the eyes separately and then give it its own spot in the texture map. Then unwrap the entire head by itself (cylindrical works best), and put that in the texture map in its own area separate from the eyes or just give it its own texture, and then the other body parts in the same manner.
High quality umapping software like DeepUV, UVMapper Pro, and the ones integrated in high-end commercial software have a lot more tools that give you the ability to unwrap your models with minor warping/deformations. I recommend looking towards trials or free alternatives to uvmapper classic if you want to get good results faster for complicatd models.
Good luck!
