Yes, the needles can stick closed, we have been seeing a LOT of problems with them in recent years with this modern fuel. Unless they are Viton, they may completely fail, or get "gummy", stick, cause flooding, etc.
The other problem we see is that the correct fuel inlet seats (diameter of the orifice) are NOT being supplied with any over the counter kits, and even today they put rubber parts in them, despite the fact that ethanol is in just about every gallon of gas sold no matter where you live.
At least once a month we'll buy kits from the local parts stores, just to check out the contents. Just a few weeks back, we purchased a new kit from a leading parts supply store (National Chain). It was for a 1971 Pontiac carburetor.
The kit contained a soft white accellerator pump with a black rubber seal on it. We submerged the pump in fresh gasoline, and in 30 minutes it has swelled up enough to easily fall of the pump.
I checked it today, and it was at least twice it's normal size!
Folks also believe because they find a "blue" seal in the kit that they are safe. Not so. There are at least 5 grades of the blue pump seals, and the light blue ones typically found in over the counter kits are "soft" and will swell up/rip/tear/fail in long term contact with ethanol.
Our kits contains the best grade of VitonĀ® fluoroelastomer, dark blue in color and ethanol compatable.......Cliff