Some facts and myths and the root of the myth.
I hear a lot of folks "You should not leave the batteries connected full time when on shore power" or "You should not be plugged in full time"
Years ago there was a converter. Magnetek 6300, among others, that was very popular in RV's.. this used a "Ferroresonate" transformer to more or less control the voltage out.. Not all that good at it.. IT was a converter/power supply putting out raw unfiltered rectified AC for lights up to around 35 amps and about 3-5 amps DC to the batteries, which filtered it, for loads that like a clean diet. (Radios for example)
Voltage regulation was not that great and when the batteries were "Full up" It kept right on pushing (Overcharging) and woudl often boil batterie dry in 1-3 weeks.
They don't make it any more.
Modern converters come in 1-2-3-3+ stages (That's in increasing order of Fantastic) The parallex 7300 is a single stage.. Now these can be tricky because if they are set properly then the battery only gets to about 90-95% charge. Not great but not all that bad.. Set a bit high. Well see Magnetek (By the way Parallex bought Maganetk out or so I'm told)...
The Paralle 7300T (yes just add T for Two) is a Two stage charger (Sorry can't resist a song reference. Tea for Two and Two for Tea....)
It, when first powered on, starts a timer and goes into "BULK" mode till the timer times out then it drops to float Bulk is a slightly higher voltage (14.6?) to push more current into the battery Float is about 13.6.
Then we have modern 3-stage.. and 3-stage plus
These monitor battery voltage and current draw.. They go into BULK when the batteries are low to quickly fill 'em to around 90%. then drop to Absorption (Still higher than 13.6 but lower current) and finally drop to float....
Now the PLUS models also do equalization.. Some under manual control some (Progressive Dynamcis wizard) does a sort of automatic equalization after I THINK 20 hours of float (NOTE The word THINK. might be off).
By the way I highly recommend Progressive Dynamics Wizard controled converters.
ALl of these.. You can plug in full time
MINIMUM time to recharge batteries is six hours.. Might be longer