SLA battery constantly being charged and used
You aren't really charging and using it at the same time in reality. This is the same when you use your smartphone, whilst plugged into a charger.

Any power required by the system (in this case the motor, and your aurdino board) is taken from the power input (the smart battery charger input). Anything remaining in the power budget is then used to charge the batteries. This means you are charging the battery, but powering the system straight from the main input and not the battery.

The trickier situation is when the power required by the system is greater than the main power input. In the common example is when charging a phone from a PC (only 500mA) and the phone is using more than 500mA (especially common when using GPS). This situation requires sourcing power from the battery at the same time as using main input power, and is requires some kind of load balancing. In this situation the battery is not charging - it is discharging.

This has no real impact on the battery life, beyond the usual charge/discharge fatigue you would expect.