That Noco model is a boost emergency-start device, not a battery charger. Advice to keep it in the car for emergencies is good.
With a trickle charger connected, you (probably) don't need to disconnect the battery from the car. Every now and again the car checks the 12V voltage and will switch on its DC-DC converter for a boost if it thinks it needs one, but if the battery's already under steady charging it wil just discover that more's not needed and go to sleep again.
I firmly suggest, though, never to use desulphation (sometimes labelled repair or pulse) charge mode unless the battery is disconnected from the car. That pulses a quite high voltage into the battery and, if you're unlucky, could cause very expensive electronics damage to the car; even if not damaged, the car's many little computers might go temporarily insane from their unstable pulsing power and need fault codes resetting. Normally just disconnect the negative terminal and clip the charger to the bare battery post.
Just checked my spreadsheet of battery voltages... the significant difference (for a car) between a standard and an AGM battery is that the Uo (initial, fast boost) charging voltage can be up to 15.0 volts for a standard battery at 20C but only 14.4 volts for AGM. If you fit an AGM to a non-AGM car there's a possibility the battery's working life will be shortened by over-charging, and if the other way about, the battery's life might be shortened by charging too slowly.
My suggestion for most EVs is that at the first sign of a 12V battery getting tired, if it's out of guarantee and over 3 years old, replace the battery. If that's a DIY replacement for ÂŁ100 every 5 years, the cost per year is probably less than running the battery for longer until you have a car that won't start, in the least convenient place and at the least convenient time.