UPDATE: Adventurers League changed the "+1 rule" in 2021.
An announcement from Q1 2021 gives the details. Basically, Adventurers League players may now simultaneously use any and all of the following sources when choosing player options like races, classes, subclasses, feats, spells, and backgrounds:
Volo's Guide to Monsters
Your intuition is sound.
Your basic AL adventures are entirely episodic, short, and fairly simple and straightforward. They incorporate no backstory, limited foreplay, and a lot of old-fashioned dungeon crawling.
So your AL character should not have a backstory that requires any playtime, and should be oriented more toward effective fighting. Too much of a ...