Yes, it's possible.
But it can be done more simply than you propose.
Using the LT1618 you need
2 x NimH cells to meet the minimum Vin spec,
3 cells to meet the maximum switch and duty cycle spec and
4 cells would be wise and still may be marginal with worst case component specs.
5 or 6 cells are really needed to be sure of an in spec design!
When designing it is essential to use the worst case values of data sheet specifications so that an in-spec component will operate as intended. If the design is one-off and you are prepared to pick amongst a batch of ICs you may be able to use typical of best case values, but this is unwise and can lead to problems with other parameters.
An example here is the LT1618 internal transistor switch current rating.
This is rate at 1.5 / 2.1 / 2.8 A minimum/typical/maximum. In many cases you may find that the switch will handle 2.1A acceptably well, but SOME devices may have a 1.5A limit and still be "in spec" so 1.5A should be used for design. Similarly, NimH cells may provide from about 1V to 1.3V out so operation with say 4 cells from 4V to 5.2V should be possible. In fact a fully charged NimH cell will have a voltage of about 1.35V when first used and immediately out of the charger may approach 1.4V. While the 1.4V output will be present only very briefly, it means that eg 4 cells can supply ~= 5.6V at no load and use of a device with an eg 5V upper limit may cause failures for reasons which would not be apparent. That does not apply here but is the sort of thing that a designer must be aware of.
[As another example, Alkaline cells have a potential of about 1.65v when new so a 4 cell nominal 6V alkaline battery can measure 6.6V at the terminals when new].
The LT1618 claims to be a constant voltage, constant current boost converter.
For this to be true the load would have to assume a single specific value as
Rload = V_constant/ I_constant.
What it in fact does is to implement a traditional CV/CC power supply where output voltage is no more than Vcv when I load is less than Icc and Icc is never more than Icc so that voltage out decreases if necessary to limit Iout to <= Icc.
When driving an LED it is usually adequate to simply control Icc and allow Vout to assume whatever value is needed to achieve this. If the LED is removed or goes open circuit Vout would notionally rise indefinitely and a simple secondary voltage control can be used to limit Vout to some value somewhat above what would be adequate to provide Icc in the intended load.
eg in your case if I_LED_desired is say 0.25A and VLED_nominal = 12V at this current, then limiting Vout to ~~= 15V max with no load is adequate, and ILED will be limited to the desired 0.25A when the LED is connected. It is 'desirable' that any output capacitor which is charged to Vout max when the LED is removed does not contain enough energy to damage the LED when it is connected if the capacitor is charged to Vout_max.
Use of the LT1618 is entirely acceptable for this purpose if desired with Vcv being set to slightly above L_LED_max at the target current. The LT1618 has an operating range of Vin = 1.6V to 18V. A NimH cell has a useful minimum output voltage of about 1V so as 2 x 1V > 1.8V, 2 cells is notionally enough.
The IC's switch maximum current limit is 1.5A minimum.
Desired output power >= 12V x 0.3A = 3.6W.
Input power is Pout / efficiency
say use 3.6W/80% to start = 4.5W.
Switch on/off time ~= proportional to 1/(Vin:Vout).
At 100% duty cycle a 2V minimum supply could give 1.5A x 2v in = 3W, so 2 cells is not enough.
3 cells gives 3V x 1.5A = 4.5W at 100% duty cycle.
At 3V in, 12V out ton:toff of switch = 12:3 at 100% efficiency = 12/15 = 80% on duty cycle.
Max switch duty cycle = 88% min (page 2) so 3 cells is about enough but somewhat marginal.
4 cells ensures that switch is well inside duty cycle limit, Iin peak can be well inside Iswitch_max and efficiency will be higher at higher Vin.
So a good choice is 4 x NimH cells with operating voltage of 4 x (1V to 1.3V) = 4V - 5.2V.
So with 4 NimH cells.
Vbatmin = 4V say.
VLED = 12.5V max say
ILED_max desired = 0.3A.
Power_LED max = 12.5 x 0.3A = 3.75 Watts.
Efficiency is uncertain, but a look through the various example circuits and efficiency curves suggests that 75% efficiency MAY result and that higher is a bonus.
Use 75% for design.
Vin = 4V, Vout = 12V (close enough to make figures tidy)
Vin effective for duty cycle calculations = Vin x efficiency = 4 x 75% = 3V.
Ton:Toff limiting = 12V:3V = 12/15 on = 80%.
Power in = Power out/efficiency = 3.75W /75% = 5W.
Iin = Pin/Vin/dc = 5W/4V /0.8 = 1.56A
Ipeak with linear ramp = 2 x Iavg = 3.12A.
We have (potential) problems - if not actual.
The worst case assumptions have ganged up to produce a load which exceeds the switch current IF I_inductor falls to 0 on each switching cycle.
A look at the photo of the oscilloscope trace at the bottom left of page 13 indicates that the converter operated with I_inductor always well above zero in a circuit the same as the one intended.
Will it work? - Probably yes, but it's marginal.
An IC with somewhat more switch capability and ability to CC regulate would be preferred BUT the LT1618 is a nice IC if it does meet the need. Reducing I_LED to say 0.2A and devices which do not fall in the worst case spec would make it safer.
OR use even more cells - probably 6.
who would have thought!
ie I may have made a major blunder somewhere. I hope not. Do point it out if I have.