It would not be a consideration for me when purchasing a rifle. You can purchase one later and have a gunsmith cut it at a pre-determined depthto fit your exact needs. recoil pads don't make a noticeful difference in recoil, but that's my opinion. Others may differ.
If you're going to be wearing heavy clothing when you hunt,put the jacket on when fitting for the recoil pad.. :

Yeah, that makes sense. I think that an extra pad in the butt is going to be good for me anyway, because when I was at the gunshop hefting various rifles, they all felt a little "crowded" to me. I do have long arms (36" sleeve in shirts), and it seemed as though it would have been more comfortable to have the trigger about an inch or two further from my shoulder. (Is this distance called the "pull"?)

Sims Vibration makes a Limbsaver recoil pad that is the best (IMHO) on the market.

I have one on every shotgun and centerfire rifle; they do indeed make a significant difference in the amount of felt recoil.

OK...thanks for the recommendation. So the question is, when rifle shopping, do I have to take this accessory into account? I ask because Remington makes their own recoil pad, but it only fits a handful of their rifles (specifically not the CDL that I was looking at).

Buy your rifle first. There are recoils pads available for everything fired off the shoulder.
http://www.lymanproducts.com/pachmayr/ -

Last fall, I bought a new Remington 700 SPS stainless 30-06, complete with 24" barrel, LimbSaver Recoil Pad, and sling for $469 at Sportsman's Warehouse.

Remington's R3 technology recoil pad is none other than that from Sim's Vibration and is a win-win situation for both companies.

Man...that's so much cheaper than what I see at my local shop. The CDL model is about $700...I'm sure the SPS is higher, if I can even get it in a left-hand model.

I'm going to have to keep my eyes open for a better deal, I can see...

Remington's new SPS line replaced the ADL model and comes with a plastic stock and comes in blue at $398 or stainless at $469 at Sportsman's Warehouse.

My local Walmart can order the woodgrained CDL for around $603 and Sportsman's Warehouse should be competitive too.

I believe that the overall weight of the riffle you are looking at is also important when looking to tame the flet recoil of your shot. With some of these feather-weight riffles now on the market you are going to notice a big differance in recoil compared to a full size riffle.
I picked up a winchester mod. 70 in .300 win mag this summer, it came with a Hogue stock equipped. It weighs a ton compared to my other long guns, but it can be almost pleasant to shoot because the shear weight seems to absorb alot of the felt recoil. The pad on the Hogue stock also is one of the best I have ever used. If you don't mind using a synthetic "rubber overmolded" stock, then you might want to check this set up out.