Is there any quick test I can do to see if I can innately determine tones like this? If I fail said test, I can know that I'm not cut out for guitar.
There are a bunch of ear training quizzes online and I believe also YouTube videos.
I don't think this is a general requirement for learning the guitar. It's just one aspect. For most people whether you can hear that something is a 3rd or a 5th shouldn't impact their ability to play songs and have fun on the guitar. A sense of rhythm is maybe more important. If you can whistle a tune or sing along anywhere close to a song you're probably ok.