yes but with caveats
firstly any awkwardness you present will be reflected back twice over, creating a feedback loop
so you really need to keep calm and friendly (a sort of 'this isn't a big deal so whatever the outcome I like you guys' additude), also if there's girls/boys around some may see you as a threat to their advances so friendliness is extra key to show you don't want to compete, just temporary companionship.
second any group has it's own dynamics at play and walking up to a them results in 10000 judgements on whether you fit in this group or not. so you're more performing for the first 15mins or so. there's alot you need to tell here through speach and body language. what do you do mean s what's your passion in life? what do we have in common? what's your particular mental illness? are you looking to murder people? this is where humour comes into play, funny stuff is relaxing. sometimes a joke can be so bad it's good. if they're memers maybe you know of a spicy new meme, or tv show. also you guys share the collective stress of school so there's always that to bring you together. also everyone poops, everyone watches shows in bed, everyone jerks it. we have much more in common than we realize.
jumping straight to a hangout is a bit much, if you want you could start of with a question, you don't understand this thing. sit down, get some help. they feel good for helping you and you owe them one in a way. a quick bond-forming activity. grabbing coffee is the most non-hangout hangout activity so that's a logical progression.
to make friends friends requires a certain amount of random encounters, you can't force being friends, it has to happen naturally.
anyway there's tons of factors and interpersonal skills are hard to learn cause you need a person to learn from. but just like most things, it looks hard at first but gets easier and easier as you try more and learn more. good luck, science bless