Theoretically, you will not damage anything by adding a DISCHARGED capacitor instead of a battery.
Danger arises when you start charging: a battery limits the voltage to its max charging voltage, even if you keep on charging after they are fully charged (with a low current like solar cells deliver). So 2 NiCds or NiMHs limit the max voltage to about 2.9V.
A capacitor does NOT limit the voltage (unless it breaks down dur to overvoltage..), so it will charge up to the max voltage the solar cells can deliver under "no load" condition (IIRC 0.45V per cell; how many cells does the Synchronar have?).
Anyway it will not work.
A capacitor's voltage decreases linearly with its remaining charge, whereas a battery delivers fairly constant voltage.
Example: battery and capacitor both charged to 2.8V = 100%
Battery discharged to 50%: 2.4V - watch still works
Capacitor at 50%: 1.4V - watch does not work.
Say the watch needs minimum 1.8V and the solar cell charges to max 3.0V (still safe for the movement, but most GoldCaps have their limit at 2.5V).
So you can only use 1.8/3.0 = 60% of the capacity, e.g. 0.6F of a 1.0F capacitor.
Now let's calculate the "Farads" of a 50mAh battery:
50mAh = 180C (=Coulomb) of charge; 1C = 1A x 1s
To get this with a capacitor by discharging it from 3.0 to 1.8V (1.2V) you'd need a capacity C = Q/U = 180Coulombs/1.2Volts =
150Farads !
Even if you could use the capacitors full charge (discharge down to 0V) you'd need 180C/3V = 60Farads
Say you have 2 Farad capacitor charged to 3.0V.
How long can it deliver 20mA (LEDs on) until voltage reaches 1.8V?
We have a charge of 2F x 1.2V = 2.4C
2.4C is 2.4As = 2400mAs -> T=2400mAs/20mA =
120 seconds until the lights go out
(I hope this wasn't too much detail)