When I take a picture using my iPhone's camera, it attaches the current location to the image in the metadata. Does it also do this for screenshots that I take?
According to macosxhints iPhone screenshots have no EXIF data, so no geolocation data would be saved. Not sure if this is still the case on the iPhone 4.
Screenshots are saved as PNG files on the original iPhone and the iPhone 3GS (the two models I had access to) and have no EXIF records. The only other metadata fields available are filename, file size, and modified, and imported dates.
iPhoto will not show screenshots as geotagged. This does not mean the information is not there somewhere, but it's highly improbable.
Checked today on iOS9 and geo data is still not stored.
I just checked EXIF Metadata of screenshot took on iPhone using EXIF Viewer by Fluntro App. Screenshots in iOS are not geotagged. (As on iOS 12)
Like what mentioned in previous answers, Screenshots are saved as PNG file and doesn't store location coordinates.
Disclaimer: I have developed the EXIF Viewer by Fluntro App :)
To know more features about the app, checkout https://www.youtube.com/watch?v=ycz0b0uDn9A