Are RAW images by nature slightly blurry prior to processing? If I open them up in Lightroom and zoom into the photo, my photos are not tack sharp but a bit blurry. Once I process, it comes out looking pretty sharp.

Wait wait wait — let me stop you right there. When you open up RAW files in Lightroom, you are seeing a processed image. Lightroom does not have a RAW data viewer, and the unprocessed RAW data doesn't look very interesting even if it did. (See What does an unprocessed RAW file look like? for more on this.) What you're seeing is either a JPEG preview (processed by the camera) or the default processing you have configured in Lightroom.

It sounds like the settings for that default rendering include less sharpening than you like. Behind all of this is your fundamental question: is sharpening a necessary part of a RAW workflow (assuming sharp images are desired)? The answer is yes — see Why should my last post-processing step be sharpening?, which is partly about the order but also gives some explanation as to why.

Digital cameras (with the mostly-obscure exception of Foveon) use a pattern of colored filters to create color images. This means color in the final image is produced via algorithms which infer complete color information from neighboring photosites. A final sharpening pass usually makes the results of these algorithms more snappy. And, although it's less common now that higher-resolution sensors make it less necessary, many digital cameras contain an (optical) low-pass filter, which intentionally blurs the image slightly to avoid moire. (See Why is a physical anti-aliasing filter still needed on modern DSLRs?.)

Additionally, digital sharpening (especially the magic that is Richardson–Lucy deconvolution) can compensate for other sharpness factors: missed focus, soft optics, or even motion blur.