Going Idle during a war and coming back

Simple answer, is yes you can.

Clash of Clans can't force you to stay on your device! You can get off, get some coffee, go have a drive, come back and still be able to battle!

Excerpt from the FAQ:

What happens if someone in my clan isn’t active in a war?
Inactive members are treated the same as active members in clan wars. They can still be the target of any actions during the war, including receiving donated troops and being attacked by the enemy. Inactive members will still count toward the total team size and their war bases will still appear on the war map. However, inactive members will not use their attacks and will not receive any bonus loot. (Obviously because their idle) As long as you still fit the requirements to battle, you can. At anytime (during the battle day).

Leaving clan and coming back during a war

Well, this on the other hand, you should never do.

If you leave during prep day and come back before battle day, no deductions are counted.

If you leave during battle day, you get no loot or bonuses at all, and obtain a shiny two day cooldown to be fight-able again.

(As proved here)

If you leave during prep day and join back, nothing changes
(Prep day)

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Nothing. No credit for the win. No war bonus loot. And 2 day cooldown before your eligible for another war.
(Battle day)

So be very careful what you decide.

See here for Frequently Asked Questions on this topic.