No, those are not likely pixels added by the computer. The original photo is made of pixels. The only way to tell if those will be visible in a print is by determining what the print resolution will be.
If you are looking at a photo at 100% (1:1) and you are seeing jagged edges, you either cropped way to much, or it's a JPEG image and what you are seeing is MCU's (Multiple Coded Units), not pixels.
MCU's are 8x8, 8x16 or 16x16 pixels squares made when a photo is converted to JPEG..
Image sharpening is a fairly complex subject.
The goal is to control edge halos. Part of that control has to do with the frequency of the image that will be sharpened.
The photo of a stand of leafy decidiuos trees would be a high ffrequency image wil require much different sharpening techniques/settings than a low frequency head and shoulders portrait of a flawless skinned high school senior girl.
ACR (Lightroom/Camera Raw) can only do 'capture' sharpening. Photoshop has the tools, features, and functions needed to do the wide range of techniques used for 'local' and 'output' sharpening.
if you don't have it already, get the book written by the guys that wrote the sharpening program used in ACR 6/ACR 7 (CS5 Camera Raw/Lightroom 3/4) -
Real World Image Sharpening with Adobe Photoshop, Camera Raw, and Lightroom (2nd Edition)