Can I get all the energy from a PV system if it is only hooked up to a CC and batteries?
Lead and lithium batteries finish their recommended charging on a constant voltage, reducing current regime, with termination at a current threshhold. Both these chemistries therefore can absorb less power at the end of their charge. Nickel batteries can be run at a high charge rate throughout and terminate on temperature rise or voltage plateau/drop.

If the potential output of your solar panel is larger than the batteries can absorb at any time, then you'll just have to 'waste' that power, by not using it. Unless of course you can find another use for the spare power, like powering a bitcoin miner, or pumping water uphill.