Emergency lighting solution
"That depends."

12V/18Ahr SLA battery should not be discharged deeper than 50% if you want it to last a long time, so I'll consider it a 9Ah battery. 

That is only 100 W, you have a 50W light, and the inverter will also add losses, so battery life will be less than two hours.

If a blackout occurs during the day, and goes on into the night, the battery could be drained before it gets dark and you actually need light. So it could be useful to add an ambient light sensor to only turn the light on at night. A PIR motion sensor to only turn it on when there are people around would also increase your battery life. You could also use a PIR sensor to turn on a powerful light, and leave a low-power light on continuously. Note that such mains powered motion/light sensors tend to use capacitive dropper mains supplies which do not go well with modified sine wave power.

The inverter will use power even if the light is off. Probably something like 5-10W if it's a cheap inverter. So if there is a blackout, the battery will drain even if the light is not used... If you don't use sensors this is less of a problem, but your charger will still have to waste power to compensate for the inverter's idle power. So, in your current schematic it would be more efficient to put the relay between the inverter and the battery.

IMO a better option would be to get rid of the inverter and use a 12V LED floodlight instead. These are common and quite cheap due to high market demand (every pimped-up truck has at least one) so look for the terms "12V led bar" or "12V led flood". You can get cheap 12V motion detectors too if you need them.

This will be more efficient as voltage will only be converted once rather than twice, there will be no inverter losses.

You will need a low-voltage cutout to make sure the battery is never over-discharged as that will severely shorten its life. You can make the cutout latching or non-latching. In your case, non-latching is probably better if you want it to work without having to babysit it. "12V battery low voltage disconnect" and sort by price on Amazon gives results.

Even if you use the inverter, it is important to check it has a low-voltage cutout too! If it does not it will kill your battery.