I just want to confirm that EC essentially affects brightness before the image is captured, whereas "Brightness" essentially affects the brightness after the image is captured.

Basically, yes. But it is not exactly that simple. It also depends on exactly what stage in the processing pipeline is "captured." Whether you mean "captured" raw data or a "captured" JPEG image produced using that raw data determines whether the more complete answer is "yes" or "no".

Short answer:

• If you saved an NEF file containing the raw to your memory card the answer is Yes.
• If you only saved a JPEG to your memory card the answer is No.

Aperture and shutter duration determine how many photons strike the imaging sensor. That is, they control how much light the camera collects. Of course, the brighter the light in the scene is, the more will be collected by the same Av and Tv. Well, unless you're considering a flash strobe that has a very short duration, in which case the Tv won't matter (unless it is shorter than the camera's sync speed in which case it will matter) and only the Av will determine how much of the light from the flash is allowed into the camera. See how quickly it ceases being so simple?

ISO and the camera's signal amplification determine how the electrical charge created by photons striking the sensor are translated to digital data in the form of what we call raw data. Everything else done downstream of the raw data is based on these digitized numbers. Changes made to the way these numbers are interpreted don't change the numbers themselves, they just change the way the numbers are processed to produce a viewable image.

The preview you see on the camera's LCD right after you take the picture is a jpeg preview generated by the camera based on the camera's firmware that includes algorithms used to convert the numbers in the raw data. Things such as black point, white point, color temperature and white balance, contrast, etc. are determined by the algorithms used to demosaic and convert the raw data. The jpeg preview, along with a list of the instructions used to produce it, is then attached to the raw image data in the NEF file.

What the various Picture Controls on your camera do is alter the set of instructions the camera uses to interpret the numbers in the raw data to create a preview image or a finished JPEG. Canon calls the same thing Picture Styles.

• If you are only saving your images as JPEGs, the Picture Control settings used when you took the picture are "baked in" and can't be reversed later. So in a sense, these settings are "captured" in the JPEG image. Any changes you make when editing a jpeg image are based on the result of the Picture Control Settings used to create the original JPEG.
• If you save the raw data, then the Picture Control settings affect the list of instructions saved alongside the data from the sensor. But they have no direct effect on the raw numbers themselves. The instructions can be altered later and a new interpretation of the same raw data can be used to produce a very different jpeg than the original interpretation produced in the preview image.

If we decide later to edit a raw file what we change are the instructions used to convert the numbers in the raw file. Even when we "save" these changes to the raw file we don't change the numbers in the original data obtained from the sensor. What we change is the set of instructions included with those numbers.

If, on the other hand, only the information in the jpeg is preserved then any further edits change the numbers contained in the jpeg file. But since the jpeg has a lot less information than the raw data did, our ability to change the image is more limited.