No he's asking if you can hardwire the analog stick directly to the motherboard.
Yes you can hardwire it. can you set the analog directly on the motherboard and solder the two together, sure but the analog won't be at the right height and you would seriously risk ripping up some pads because the analog wouldn't be screwed into the faceplate. the system was designed the way it was for a reason. I recommend you actually take the time and brain power and actually properly trouble shoot the issues you are having with the analog and then fix it from there. don't just hardwire it.