Yes, you can and it is indeed possible to create a jpg file tagged with AdobeRGB color space.
A wider color space will result in fewer "extreme" color values reaching the edge of the color space, which translate in better differentiation between those saturated/bright colors.
sRGB is still recommended for web images though. On the other hand, print or display on some displays designed for critical color work will benefit from using AdobeRGB.
Besides, all the manipulations you do on your images in applications like Photoshop benefit from an even wider colorspage, typically Prophoto to further reduce the risk that some intermediate image manipulations may result in color value truncation.
You should invest in some books about basic color management, they all go through this in minute details with explanations way better than mines.