Yep. All you have to think about is how much damage you'll do with the effect compared to your regular damage. Cait is the same in that her passive comes secondary to her main source of damage : auto attacks.
Even if you ignore her other abilities which scale with AD, she'll do more damage with the extra AD, even if she's standing in a bush which would trigger the effect every 4th shot. While that extra shot damage is nice, think of it as icing on the cake - you like it and it's good but that's not the main thing you're after. In most things in this game there's a balance. You have to balance health versus defense for example. If you go all defense and have 600 defense, that's much worse than having like 350 defense and more health items. At about 400 defense, more defense doesn't really help so after that you go health. The same way though, you'll be able to take less damage if you go pure health. It's a bell curve sorta deal.

This same thing applies to AD versus AS. If you go all AS that would be an awful build, pretty much the same if you went all BT. You need a balance to get optimal damage output. The trick is finding that optimal range and when you should get what. For the most part, getting damage early is better for AD carries since that boost in damage will be better than a boost in AS. It's all about the bell curve.

As a side note though, at the same time you might want to go all damage and AS but if you're too squishy, you'll die quickly. If you die quickly, you get less attacks in and do less damage. That's why it's often good to get items such as a Banshee's Veil or a GA on carries, that's another bell curve sort of thing. Too much tanky, you don't do damage, too much offense and you die right away. It's all about finding the balance.

I don't have actual number to show you but I'm sure someone online has graphed it if you want all the details. (Maybe I should make a guide with this info, hahaha)

tl;dr You need to balance it. Early game damage is better than early game AS usually (in my opinion)

The best starting item on any ADC is hands down (and nobody will argue with me on this) wits end for 4 reasons:
MR
Attack Speed
On hit
Health

I should hope so; IE cost 1k gold more. Attack speed does more damage over time, and if you are standing still trading blows the entire fight attack speed is better.

The problem is, that's not how this game is played. You usually try to get a couple attacks in and back off - in which case having higher dmg for 1-2 auto attacks and a special would cause more damage. That is typically why ranged ad carries go for IE first, then PD.

Overall the best build is to get a BF sword, then build a zeal and finish with IE for the most damage supplementing the build with Doran's or a Vamp Cepter when/if needed. This is done because without high AD attack speed won't mean anything as it is just a flurry of pinpricks and crits do 200% of your damage and if that is low so will your crits be.

I'd say that boots,dorans,dorans,vamp scepter,bf sword, ie or bt, then zeal is the correct build path for ranged ad carries like vayne and cait. boots 2 somewhere in there.. Anyways with most of them you want to hit hard asap... vayne and kog are the 2 that come to mind that an argument can be made to go for pd first.. I dont, but its not exactly wrong for you to do

I've considered that but came to the conclusion that it doesn't synergize with crit or armor pen so its not the best choice offense wise... then its not the best choise defense wise when that slot could go to qss, ga, or maybe banshees