Nah!! Not the worse...the more informative!!!
Likely it does leak air some, but any airleak that causes stickage is more likely to be seizure..not simply mechanical throttle binding. That missing gasket will be ASKING for some kind of grit to stick your slide, though.
DO replace it.
I suppose, in the realm of complete conjecture, that the missing gasket could cause the slide to come up too far..the needle getting out of the needle jet..and THAT keeping it from dropping back down. Doubt it. You could look down the throat of your carb, wick it open to ensure the needle doesn't completely clear the needle jet (what it regulates pretty much).
I adhere to the 'Fix what you know is broke!' postulate. Heck, it may even be a theorem!! Many times I've come across something not right in the process of trying to sort out 'some other' (I thought) problem. Lo and behold..fixing the 'somethng' took care of the 'some other' problem.
'Wing' meaning, based on other 250 pics I found on the web, the distended part of the tank that adds to the overall volume of an 'oversized' tank.
Look at YZs and some katooms for example. The 'subtanks' practically cover up the cylinder! ..I don't know how fuel gets from one side to the other on those things. YZs don't have a crossover tube.....
Looks like you would have enough room to run a curved tube (and its associated parts).
I'd be fixing the missing gasket first.
Looks like you got the 'unassisted pic posting' part down!

See? Things ARE progressing..and there's learnin' in the process!!
A complete aside..but...
My honey's Banshee throttle had a sticking problem. Two or three cables, some correspondence with MotionPro that ended up in their fixing their faulty throttle side termination, re-routing, carb body
replacement! (Thank you Mr. Black!) cleaning and multiple carb resyncs later (Banshees are twin cylindered), the last trip to the sand showed the problem to be gone. What was it? Not sure. There was some grease in the cable splitter I cleaned out and I took off the electrical tape I'd thoughtfully wrapped around the splitter in an attempt to keep moisture out. It wasn't wrapped tight, but maybe it caused some interference inside the spliiter (one-to-two cable device).
The point of the fable is...it took a few months to get it..but it's got now, I'm fairly confident. A WOT stuck Banshee just might soil your drawers!!
You'll get it. Keep after it, and: You will learn a lot about your bike, AND it will be FIXED!!