Yes, I would guess that the capacitors would hold energy for say 12 hrs, so you still need a big enough power plant to run your drives and computers (otherwise you could charge batteries at a starport and use them for your Jump drive and possibly scale down your PP size).
Given the sensor ranges and time to approach your target, you could charge some batteries off your power plant. Most use for small fighters who want to carry lasers etc. You can charge the batteries just before launch (carriers usually have large PP to their JD which are not fully used in combat) and use them to power the weapons.
Given the survival chances of small sighters and the 12 hr limit of cockpit occupancy of 12 hrs or 36 combat turns, 1 tn of batteries gets you 36 shots with your BL at 1 shot per combat turn. Seems to match nicely.
It seems a nice idea, for those small fighters. We must think that the cockpit may have LS for 12 hours, but I guess Pilot performance would start to drop well before that (I think about half this time is even generous, mostly for single seat fighters, most so in combat situations), so 1 dton (1.5 perhaps) of capacitors may well feed a fighter's weapons, MD, computer and some agility for those 6 hours, making it a sound alternative. Worth thinking about that...
Using batteries to power weapons is only really useful for small fighters at TL12- as PP take so much space at these TL levels. Bigger figthers can carry the necessary PP, and high tech ones have more efficient plant.
Also useful for emergency conversion of merchants into SDBs / escorts - Thinking TNE here. Such merchant vessels never have a big enough PP to run their drives, computers and energy weapons, so a battery they can charge up as the enemy approaches, which then powers any lasers will be useful. The only problem is their poor sensors may not spot an enemy until it is on top of them. But a few rounds of laser fire from the battery whilst still having agility, is better than laser fire from a stationary ship.
But here we're talking about a 1000 dton frigate/corvette with energy TL 8, just trying to reduce a fision PP due to its high cost/engeneering crew demands. Sensors are only TL 8/9 too, so you cannot rely on having advance notice of the battle as to charge your capacitors, so, IMO, you should rely on batteries, if you accept to limit your laser bateries to 1 hour of fighting, depending on missiles for the rest of the combat. Of course capacitors are assumed to be available, as the ship has jump capability (space TL 9).
Accepting your premise (capacitors are able to hold energy for about 12 hours), and with little spare power ito recharge it, you need more than those 12 howrs to recharge, unless you can shut down your MD for about one hour and a half and use the power to recharge them, I don't see them as an option.
Batteries, on the other hand, can store the energy for long time, so you may recharge them while in jump (you don't need your MD there, and even if you'd need to keep it on, you have time to spare), or after the battle, not having to stay 'dead on space' (MD off) just when you detect possible hostile ships for your lasers to have any worth.
