What happens if you forget to unplug? My son did this and now has removed the retaining lug on the lid of the 16A socket so if he does it again the plug will just pull out. And unlike driving a car he stands at back right next to cable and still forgot to unplug.
I have seen fire trucks with both charger and water heater so even if not used for months they can still spring into action and because of water heater they had mains supply. But to float charge a battery there is no need to have the mains supply the 13.8vdc supply is good enough. To maintain a battery even the 400AH used on my sons boat only needs about 0.5A and even when old 1A is plenty.
But 14.7v is what is considered as bulk charge voltage and not float so to reduce the voltage is likely a good thing.
The voltage to a lead acid battery is normally considered as:-
13.8v - Float the battery can be charged 24/7 at this voltage.
14.2v - Often used by vehicles as compromise between bulk and float voltage.
14.8 - bulk charge voltage.
So a good quality stepped battery charger will on switch on supply max amps (25A in case of one my son uses) until the battery voltage reaches 14.8 volts. At this point the amps will be reduced to hold voltage to 14.8 volts and the amps will be monitored. Once the amps drop to a pre-set level (2.5A in case of one my son uses) or after a pre-set time has elapsed (8h in case of one my son uses) the voltage is further reduced to 13.8v. These are called "Step" chargers. With forklifts where the battery is not used while being charged the voltages per cell may be higher and and final stage switches the charger off.
With cheap car chargers they have two jobs.
1) Re-charge a battery after something has gone wrong i.e. leaving on lights so the higher charge rate the less time it will take but normally the output will not exceed 12A as above that some control is required.
2) To equalise the cells. When batteries and charged and discharged one cells may be more efficient than another so over time some cells become under charged and others overcharged so every round again the whole battery is slightly over charged to bring all cells to same level. Normally around 1.5A for 24 hours with 60AH battery topping up once charged. (Only emergency top up before as electrolyte levels rise as charged)
The charger you show is too small to do 1) and too big to do 2)
The whole idea of equalising charge is not required with modern cars as the alternator does not let the battery discharge except on engine start unlike the old dynamo where the voltage would vary from 12 to 16 volts while the car was driven so the trickle charger has gone in the main.
Best place for charger you have linked to is
what you need is something like this
link which if you follow link states "Full charge automatic switching to maintenance mode." This is not as good as type my son uses but a lot cheaper a proper charger able to follow the stepped charge like this
will start at around £100+ see
here 
but are not really needed for cars.
When CB's were common the power supplies used to power them made really good float chargers but now hard to find CB stuff.
