The 7100 is a converter that stays on. The external charger could be one of those which shuts off when it decides the battery is full, so it is no good as a substitute converter. I don't know what the SEC does for that.
I have a 7300 which is still the RV's converter for when on shore power, but I do my battery charging when off grid from generator using external chargers that have better charging profiles than the converter has, but they shut off when done. I have one that does not shut off but stays at 14.8 until I shut it off, so that is no use as a converter either.
The fixed 13.8v of the 7100/7300 converter will only gas off your battery 'water' if you leave it on in hot weather for a long enough time. The correct float voltage depends on the temperature. 13.8v is correct for 50F. Colder than that out, and 13.8v is too low. 80F goes with 13.2v.
Some AGMs specify they are to be floated at 13.8v. What AGM does the OP have?
If you live where you are floating the batts where it is below 50F, all you get by having the three-stage converter is 13.2v which is even lower than the already too low 13.8! You guys all know this but keep telling people they just have to have a three stage converter no matter where they live.
In any case, if you do have 13.8 and you live where you float the batts for a long time above 50F, you just add water to the batts every so often---it is not a big chore---and it is your own fault if you don't do that, not the converter's. :)