I have had good results with using a car charger in addition to the built in charger (which in my case is a rather useless one that will be replaced in the spring), but only to the point where the voltage increases to max when the current limiting is no longer an issue, after that of course there is no benefit and that is a fair portion of the time. You have a fairly large battery, so you may save a worthwhile amount of generator time if your two units can work with each other.
That said both units will not power up at exactly the same time, so unless you are very heavily discharged the battery will appear to be at a higher stage of charge than it is and the voltage setting may be set lower than it should be if the unit senses that higher voltage. Some units can have the voltage forced higher for a period of time, in which case make sure you do that.