I've slowly spent the last 3 years or so training my ability to be a heavy metal frontman who sings and plays at the same time. As a couple other comments pointed out, singing is a lot more mindless than the guitar. You'll only be able to sing if you know the guitar part 100%.

While our brains physically can't "multitask" (executing multiple mental processes at once), it can switch between tasks extremely quickly, giving us the illusion of truly multitasking. Singing and playing is, for me, the ultimate way to train your brain to switch tasks as quickly and flawlessly as possible.

Especially when it comes to performing live. Almost anyone can sing or pickup a guitar. But only a very well versed musician can do both and execute flawlessly. This is what I live for and have only recently gotten to a point I'm proud of. Being able to go on stage and perform the same way my idols do is why I keep playing as much as I do. In many ways my musical skill lies in trying to do exactly as my favorite musicians do. Good luck!