Curiosity question here. Would charging at the max rate have more of a detrimental effect on the battery than Level 1 charging? I got a 60a charger, which is overkill, but it was free. I rarely need/want to charge the car as fast as it's capable of being charged. I'm wondering if I should migrate to the stock charger for more routine charging. The main benefit of the Level 2 is the pre-conditioning from the grid rather than the battery. I love pre-conditioning. (tangent, is the AC supposed to cycle on/off during pre-conditioning?)
Max draw will be 32 amps, because that's what the charger (which is part of the car) is built to allow. Having a higher max on your EVSE won't change that. I don't think slowing down charging (below 32A) would change battery life substantially (Honda seems to have made some effort to mitigate degradation).
Short answer: No. Level 2 charging provides a relatively slow, safe charging rate for our lithium batteries. There are a number of variables that can have an effect on battery longevity. The difference between a lifetime of charging at L1 v L2 is one of those variables. It would fall between difficult and impossible to determine to what degree either method had on the longevity of the batteries.
The "battery degradation" you hear about is mostly do to with the overuse of DC Fast Charging, something the Clarity PHEV cannot do. L2 charging is more efficient than L1 charging - this, too, is a benefit. Honda recommends that you use L2 charging, if available. (FWIW, Hyundai/Kia actually state that L1 charging be used only when necessary in their EV and PHEV vehicles.) Yes, the AC will cycle while preconditioning the cabin - it's actually a heat pump: In mild temperatures it will also heat the cabin. In colder weather there's a resistance unit that works like an on-demand water heater to provide cabin heat.
I have 2 evse's. The Honda OEM unit and a Lefanev 32 amp Level 2 evse. The Clarity draws max 30amps when connected to the Lefanev unit. It will fully charge a depleted battery in about 2 hours. I have a custom made NEMA 6-20 cable that allows the Honda OEM unit to run on 240v power. It charges at 11amps max. It will charge a fully depleted battery in about 5.5 hours. Just throwing that out there in case you want Level 2 charging speeds without the ~$300 cost of a Level 2 evse.