If I just want some more mana regen, and I'm planning on building Morello later, can I pick up a forbidden idol and then build my first item? Or should I just go ahead and finish morellos if I'm going to get the idol?
Example: I'm playing Morgana mid and want to rush Zhonia's but need a bit of mana regen. Can I buy forbidden idol and leave it or should I finish morellonomicon?
I'd say in the specific case of buying it while wanting to rush Zhonya's, just finish the Morellonomicon. A) Morello doubles the mana regen from forbidden idol, as well as the CDR. B) Once you have the idol, your morello only costs 1700 gp, and gives 80 AP+Grievous Wounds (Which is a little more than that -100gp NLR.) And more mana and spells.
Overall, the Morello gives you a power spike earlier, at an unexpected time. It also doubles the mana sustain you are looking for. Fewer backs for OoM while using more spells=More farm. More farm=Faster Zhonya's.
As mid i've typically been building the con first - grievous wounds helps keep sustain mids (mid?) under control.
At low levels a second 
is better for mana regen and combat stats.
Look up your champion's MP5 on the wiki, find when a 50% of base is close enough to 3 per 5 seconds to be acceptable to your play style.
So I think thats a valid option to stick with only forbidden idol and eventually upgrade it later on. It depends on what item you're getting next so if your next item is rabadon's deathcap or void staff, its fine. (it should be some major ap or dmg item). But do you really want to do that when you can complete morellonomicon for only 1700 more gold which will give you even more mana regen, 80 AP, and grievous wound passive? The item is very cheap which makes completing it first a good idea.
idol itself isnt a very useful item. early on, 50% mp5 is hardly anything. the 10 cdr won't help much because you'll be oom anyways. if you want a zhonyas just go double doran ring into seekers instead.
I have several times tried forbidden idol before jumping straight into a 
for Malz or 
for Morg. It works for champions that have naturally high mana regen, but most do not. In that case, Doran's ring is better to have.
I think it is entirely valid, you don't need the CDR and Grievous Wounds until later anyway. Going towards a more aggressive/Defensive Item will bring mid game sooner. The mana sustain / anti health sustain isn't always needed. But it bothers some people to have components, they feel very compelled to finish. Which is a grave mistake 
users I see way too often.
Yes of course! Forbidden Idol can be a respectful early item, especially for cdr heavy mages at lvel 6 like Leblanc who can benefit a lot from minor mana but extra cdr. However I would recommend finishing Morello if you're going for a Zhonia style build. If you're going for heavy CDR you can finish another item first.
