Yes. It would be advisable to check the Vf of the LEDs you want to use at the current you intend to use, and hand select pairs so the sums of their Vf are as close as possible. The string with the d3mm and 5mm LEDs may need its series resistor adjusted to compensate. Also, the MOSFET source resistor will need tweaking to get your desired total current.
A further issue is the MOSFET gate threshold voltage - if its too low, the gate will charge far past the voltage required for fully On, and therefore the turnoff will be delayed and slow. This can be fixed by adding a pull-down resistor so the gate is fed from a potential divider. However the threshold voltage is not closely specified and will vary from part to part, so this circuit is really only suitable for a one-off hand built 'prop' or similar. Revised sim with blue LEDs and gate divider attached.
Edit: The sim has an unrealistically low internal resistance for the stack of CR2032 cells. 18 Ohms is in the ballpark for a single cell, but it needs multiplying by the number of cells. If your LED Vf is significantly over 3V, you may even need to go to 4x CR2032 to get enough headroom for the MOSFET. At that point it may be worth replacing the lower resistor in the gate divider with a Zener, to stabilise the gate voltage and thus the load current as the battery discharges. A few LED models may help in the future. Just paste any or all of them as a SPICE directive directly on the schematic, or save as a file and include with .lib.
*Typ IR LED from optocoupler: Vf=1.2V @10mA
.model LED0 D (IS=1p N=1.999644 RS=0 BV=6 IBV=10u
+ CJO=10p EG=1.424 TT=500n)
*Typ RED GaAs LED: Vf=1.7V Vr=4V If=40mA trr=3uS
.MODEL LED1 D (IS=93.2P RS=42M N=3.73 BV=4 IBV=10U
+ CJO=2.97P VJ=.75 M=.333 TT=4.32U)
*Typ RED,GREEN,YELLOW,AMBER GaAs LED: Vf=2.1V Vr=4V If=40mA trr=3uS
.MODEL LED2 D (IS=93.1P RS=42M N=4.61 BV=4 IBV=10U
+ CJO=2.97P VJ=.75 M=.333 TT=4.32U)
*Typ BLUE SiC LED: Vf=3.4V Vr=5V If=40mA trr=3uS
.MODEL LED3 D (IS=93.1P RS=42M N=7.47 BV=5 IBV=30U
+ CJO=2.97P VJ=.75 M=.333 TT=4.32U)
*Typ small White LED: Vf=3.2V Vr=5V If=35mA
.MODEL LED4 AKO:NSSWS108T
LTSPICE already has
NSSWS108T, which is a small white small SMD LED, with a characteristic similar to many 3mm and 5mm white LEDs.