Yep. JPGs can be .jpg, .jpeg, or .jpe.
However, as GIFs are limited to 256 colors and JPGs have up to 16 million, when you convert to a GIF there will be quality and detail lost. Also, GIFs tend to be large files, and the best way to shrink them is by lowering the number of colors, which will then lower quality even more.
So in short; no.