You should be able to perfectly deform a curve with a another curve, no need to convert to mesh first.
But raises the question why. If the second deforming curve already has the desired shape use that one directly.
Curve deformation generally works well on elongated objects that roughly extend in one direction that should run parallel to the length of the curve deforming it.
So if that is the case and the other object is elongated than you probably won't need second curve to be deformed.
Otherwise it will probably give very weird results. If your curve has a really contorted shape it will probably yield unexpected glitchy-looking deformations.
Things to look out for when using the Curve Deform modifier are
- Make sure deforming curve and deformed object are coinciding have exactly the same origin point in the scene's unit coordinates
- Make sure the deforming curve's origin coincides with one its end vertex. In other words one of the end vertex has
0,0,0 local coordinate.
- Make sure the vertex at
0,0,0 is the starting vertex, not the end one.
- Make sure the deformed object has it geometry roughly close or around it's center, or at least sanely placed in relation to it's center (like at one end).
- And lastly make sure the deformed object (the one with the Curve modifier) is elongated in the correct direction that runs roughly parallel along the curve length
If not, then you can adjust the deformation axis in the Curve modifier properties.
For more complex deformations you may want to look into the Cast Modifier, or the Simple Deform one, or even the Shrink Wrap one.