Yes, I have done builds on medium pad ships with a tiny 3A power plant. They didn't have to power any weapons or large shields.
As long as the overall ship power load doesn't exceed the Power Plant, you are good to use it.
One thing to consider, is the 50% power drop point. IIRC, in combat when a power plant is targeted and drops to 0%, it's power output will reduce to 50%. So it's key to use the power management groups (1,2,3, etc.) to make certain that your core modules (Group 1) will have power if your Power Plant is at 50% output. Anything above that should be in Group 2, 3, etc., and those would go offline in case the Power Plant goes down.
I keep these modules in Group 1:
Thrusters - Gotta keep mobility
Distributor - To recharge for boosting away
Chaffe/Point Defense - Maintain defenses
FSD - Critical, my escape hope.
Then in Group 2:
Shields/Boosters - If the Power Plant is sniped, the shields are already offline. Worthless.
Life Suppport - With an A rated module I'm good for 25 minutes, other builds might reconsider this being in Group 1.
Weapons
Cargo Hatch
...
The point regarding Power Plants and this is... This 50% balancing act might be hard on a ship with super small Power Plant and large module power draw. The boosted/engineered thrusters alone might take up 45% of the full power output, leaving little room for critical stuff like FSD.
If anybody sees that I'm doing something wrong above, please post. Certainly worth knowing and considering.
Sry but this isn't right.
If your powerplant goes to 0% integrity you have 0% energy. You're dead unless you make a restart/repair sequence to bring the powerplant back online.
These 50% power is when your powerplant experience a malfunction which will usually happens below 80% integrity.