Yes but why represent data this way when HTTP can already handle binary? Does base64 actually compress binary data enough to make these optimized requests? I'm genuinely asking because I have not googled it yet.
Base64 uses a 64 character alphabet (hence the name), so you can only represent 64 different values within each byte. 64 == 2^6, so basically you are using 6 bits out of every byte and losing the other 2 bits.
HTTP can use compression to reduce the size of the Base64 representation, but assuming the images were already using a compressed format, all this is going to do is mitigate the inefficiency, it's not going to be more efficient overall.
This mainly applies when you have to transmit binary data using a text-based format like JSON or XML. I've also used this before to build a shell-script-based installer, where a compressed archive is base64'd in a variable.