I just installed the All NPC at Begin mod. If I pick up Coran at the Freindly Arm Inn will he leave me for not doing his quest right away? If so I am gonna uninstall this mod.

Coran will not leave because of not doing the quest. He will nag, but won't leave. The only way Coran will leave is over reputation.

Ok Thanks ElfBane thats good to know. What about Safana?

But, after a set amount of time, Coran will leave, Safana as well. But if the mod has a component that stops this, then correct me if I'm wrong.

To the best of my knowledge, neither Coran or Safana will leave because of failure to complete their respective "quests". As a matter of fact I don't think either NPC cares whether you do their quests. I believe these quests are partially 'broken'. By that I mean....you 'get' the quest from the NPC, but you don't have anything to return to them for XP. IIRC, Coran will keep nagging about his quest even after you have returned a wyvern head to Kelldath.

Thanks guys but I uninstalled it because it felt like cheating. That info is good to have for when I get them in my party THANKS again.