I have that case, I wouldn’t. I’d be afraid that they would apply pressure to the screen which could bruise it. I ended up upgrading to another case with more room.
I have the same case. I just recently bought some ear buds originally for listening to music, but I decide, why not use it for traveling when playing the Switch? So, yeah, i toss my ear buds in the pouch and they work pretty well.
I've got joy-con straps in the pouch of my case (which is the same as yours) and my Switch is fine. Of course, I have a tempered glass screen protector on, but I think even without it should be fine. The padding that sits on the screen feels thick enough to prevent anything in the pouch from harming the screen.