Not just on the current setting. The voltage drop will also depend on the actual current through it, the temperature, and vary from one device to another.
Lets take a look at the datasheet. The OnSemi version has the classic 'laboratory' PSU circuit (fig. 22), and also the graph we need - Dropout voltage (fig 10)
https://www.onsemi.com/pub/Collateral/LM317-D.PDFThere will be up to 1.25V (assuming Vref is at its nominal value, and the current limit is set to max) across Rsc, and the dropout voltage of the regulator can be up to 2.5V. That means there is up to 3.75V drop across the CC LM317. At very light loads, the voltage across Rsc is negligible, but the voltage drop across the LM317 typically varies between 1.75V and 1V with temperature. Therefore the fig.22 arrangement is the only way to use two LM317 or similar regulators to implement a CC/CV PSU.
However it makes a fairly crappy PSU if you need much current, as the CV LM317 will also need up to 2.5V across it to regulate at max current, so you need 6.25V headroom from the trough of the ripple on the unregulated supply. As the absolute maximum input-output differential is 40V, the peak unregulated input voltage for the fig 22 circuit must *NEVER* exceed 41V (assuming a minimum 1V drop in the second regulator) or it will die if the output is shorted. After allowing for line voltage variation, this makes it effectively impossible to build a 0-30V PSU capable of any significant current using that circuit without a preregulator.
If you can tolerate a less precise current limit, take a look at the LM723 - With external pass transistors, its a far better choice to build a low cost bench PSU around.