Fallout – Can Raider Attacks occur while you are not in the game

The times I have had the need to "off" a dweller I just send them into the waste and let them die there. You will have the option to "remove" them once they are dead.

Just remember to send them out without any outfit or weapon.

The game has 2 different running in background behaviours:

• The game's wiki specifies that the resources will be consumed only for a little while after the game is no longer in use (game sent to background, phone not used etc). This is due to the fact that the resources require a lot of management and you would have to check/play the game every few minutes, half an hour at most, before your dwellers would start dying, get irradiated, etc
• Other activities that require a long time will still be in play (or generated once you open the game again, based on how long actually took since you last stopped playing - in normal hours) ... these activities are: wasteland exploration and returning, training, pregnancy, baby growing up, radio and creating resources
• You will also never be attacked by raiders, deathclaw or molerats while the game is on background.

As an example: A baby requires 3 hours in order to grow up and become an adult. When you open the game again, the game will check if 3 hours have passed since the baby was born to determine whether to make that baby an adult.

Warning: Players tried to fool the game by changing the timer, clock... be aware that this can cause lots of bugs, malfunctions, freezes, crashes etc

TL/DR: Yes, resources will be consumed only when you play the game or for a short while after you stop playing the game.