Yes, make your screen shots however you want them at highest quality. With most quality mobile phones these days, as well as computers with high density displays like the macbook retina displays, you want your images to be 2x the desired size. So if you are going to display an image at 300px wide, then you want the image to be 600px.
Here is an article that provides a visual demonstration of the noticeable difference in quality. On an Iphone or Samsung Galaxy, this could make the difference between a screenshot that is blurry and illegible and one that is clear.
Having done some mass conversions in the past, Photoshop has tools for automating conversions, using Automate|Batch
You should spend more time in the chrome developer tools if you believe this to be true.