Kind of...
If your ballast resistor is connected to the VOut of the LM317 to ground, depending on what voltage the regulator is putting out, the current through it will vary.
The limiter circuit works by maintaining 1.25V across the current setting resistor. That means that VOut could range from VIn-3V if the circuit is powered up and not yet hooked to your cell, to as low as 11.25V if you set your cell to exactly 10V though I'd recommend more like 12V if you can get there - a little more voltage helps rather than hurts.
The issue is, given the range of voltage the regulator can vary over, you need to compute your ballast resistor at the lowest possible voltage.
For safe area, lets say 10V in case your cell coasts a little below 10V during a run.
So, R = 10/0.01 (10ma) = 1000Ohms
OK, fine and dandy BUT when you haven't yet connected the cell and have powered up the limiter, its putting out say 21V if you're powering it with 24V as an example. So, at 21V, a 1k resistor would pass 21milliamps. Sure, no big deal, or is it?
What about power dissipation in the ballast resistor? It will be, in the 21V case, dissipating 0.021^2 * 1000 = 0.441 WATTS! You had better consider using at least a 1 watt resistor unless you want a branding iron instead. A 1/2watt WILL get VERY HOT with this much power dissipation.
Sure, when the cell is operating with 10V across it the current through the ballast resistor would be 11.25v/1000 = 11.25ma where the power would be about 0.127watts but you can't design to this - only to worst case because over time it WILL happen.
HAHAHA, this is sick but it'd work well. Make another current limiter and set it to say 12-15ma just to be safe using a fixed value current setting resistor and connect Vin of this circuit to the output of the real current limiter regulator (LM317 VOut) and the output of this ballast limiter to ground. Now, the ballast resistor only ever has 1.25V across it and even a 1/8 watt would be fine and even in a situation where the real cell current limiter regulator is putting out 11.25V, you still have plenty of safe operating area for this "ballast limiter" to continue functioning - 11.25 - 3 - 1.25 = 7V.
If for the ballast current regulator current setting resistor you used an 82Ohm resistor, that'd be 15.24ma. The power dissipation of the current setting resistor for this would now be 0.019watts (19milliwatts). Even an 1/8W resistor would do wonders and would stay cool as a cucumber.
There is a simpler solution though.
Go buy an LM317LZ TO92 packaged device and crack out of the box you'll easily be able to go as low as 2.5ma but probably even a bit below 2ma though the manufacturer doesn't guaranteed anything but 2.5ma. I bought 20 of these at the last aliexpress sale, with shipping, for less than a buck total and yeah, I said for 20 of them. They're dirt cheap but you do have to shop around a bit because sometimes, onesies will cost you as much as 20-50 (I've seen it - thats why I bought 20).