What would be the initial rate of charge for a 14.8 V (nominal) battery discharged to, I guess, 12 V when connected to a 16.8 V supply? If the charger is rated at only 1 A would this sag the voltage and just charge more slowly? Assume there's one of those li-ion charge protection circuits in place if that makes a difference. If the charger is specifically intended for li-ion charging, I guess it reacts more predictably?

 

What would be the initial rate of charge for a 14.8 V (nominal) battery discharged to, I guess, 12 V when connected to a 16.8 V supply?

It would depend on the combined resistance of the battery, the supply and any intervening wiring if the supply was not current-limited in any way. It could be many Amps!

If the charger is rated at only 1 A would this sag the voltage

Not significantly if the charger were well-regulated to 16.8V and the current were less than 1A.

If the charger is specifically intended for li-ion charging, I guess it reacts more predictably?

Yes. That's what you should use, in the interests of safety. Any other type risks fire/BOOM!/ a change of underwear.