Simple answer is YES!
Noise is an undesirable artifact, and many operations can enhance its appearance, not just sharpening. Tweaking curves, adjusting contrast, working exposure, etc. can all have some impact on the noise that is present in an image...although sharpening tends to have the greatest impact. It is important to handle the bulk of your noise reduction as one of the first steps of your development workflow. You should not necessarily aim to "eliminate" all noise...rather your goal should be to reduce the effect noise has on an image as much as possible without adversely affecting detail that you wish to keep. The tool you use to remove noise can have a HUGE impact on the results as well...Photoshop in particular is not really known these days as having the best noise reduction tools. Lightroom has some fairly excellent noise reduction, and there are other tools like Noise Ninja and Neat Image that also do an excellent job.
Keep in mind your final presentation format and size...a LOT of noise that may be present in an image at 100% is going to get "absorbed" (for lack of a better term) into the final presentation format. Prints can sometimes exhibit pronounced noise, particularly when the noise contrasts well with the base image. Usually a moderate amount of noise, particularly in smooth gradients, can be beneficial to final print output as it normalizes content and eliminates harsh transitions. Presentation on a computer screen is often best done at significantly lower resolution than the original image, and downscaling is a superb mechanism for eliminating noise. If you start out with a moderate amount of noise, or an even distribution of high amounts of noise, downscaling for display on a computer screen (i.e. via a web page) can be all the noise reduction you need.
Sharpening is a facet that is closely linked to the viewing medium of an image. Generally speaking, its best to save sharpening for last. Not only that, its best to keep sharpened images saved as separate files from your primary work image (which in turn should be separate from your original master image.) The amount of sharpening done, and the type of algorithm used and its settings, should be matched to the output medium for your photos. If you intend an image to be viewed onscreen, the kind of sharpening you do will be different than if you intend to print. The size of the final image for either medium will also affect how much sharpening you do, and how that sharpening is done. It's a good best practice to save resizing, cropping and sharpening for the very last two steps of your image editing. Duplicate, crop, resize, sharpen. If sharpening greatly enhances the remaining noise in your image, you may also want to do a final "light" pass of noise reduction to minimize it as much as you can without adversely affecting sharpness.