theoretically yes, but the price would be unreal...and also that is not the only way to do it...
If you start to mess with internals, there are a number of ways to make it smoother...but smoothness will be directly related to shift speed...An example: that Type S's first to second syncros are very grabby, making a slow shift from first to second very clunky...but when you hurry it, it snicks right in perfectly...So unless you slam it from first to second it doesn't feel great and smooth...ours feels better being slowly slipped into to second, and if we swapped out syncros for grabbier ones of a different material, it would be more difficult to shift slow and smooth, but better for shifting quickly...I know this is hard to understand...
This should compare it better...There are basically two types of manual transmissions/transaxles that differ only internally...Constant mesh (motorcyle manual gearboxes) and syncromesh (almost every modern production car gearbox)...Fundamentally constant mesh systems do not have syncros, and for the scope of this post I will leave it at that...Constant mesh setups allow shift speed on the verge of insanity, and clutch work is not even needed in some situations...during full throttle you simply ease on the gas to relieve acceleration stress, and slam on the shifter like you have pair...simple as that...Think of modern super bikes, and those crazy dudes popping through gears that seem like a sequential manual pipe dream...A lot of companies make gear sets to turn a stock gearbox into a constant mesh one, but not yet for protege's...Sentra and WRX's to name a few have this option, but they are generally regarded as racing setups only mostly becuase of how taxing they are for daily street driving...simply put, constant mesh systems have to be handled by a man...you cannot shift slowly without craking the hole thing apart...Same thing with a motorcyle...have you ever tried to slowly lift your left foot to shift? The hole thing bucks and pops and sounds like crap, but if you pull your foot up with authority everything works great...That is what you have to do with a constant mesh car...You would HAVE to have an extremely short throw shifter (not like our current aftermarket shifters, but one with about an inch or so of throw from first to second!), and only use the cluth for smoothness...every shift would have to be hellishly fast regardless of whether you are racing or getting groceries...You can slip the clutch for driving smoothness, but the actual movement of the shifter will always have to be crazy fast...
Now I realize that has nothing to do with what you asked, but sort of apply that to a syncro mesh car...Bigger grabbier syncros with more surface area will kind of behave the same way...you will gain high speed shifting smoothness, but loose lazy around town shifting smoothness...if you try to shift it smoothly the it is similar to a very grabby clutch...it will grind and bang a bit...
And also no internal mods can be found for our boxes yet other than LSD's...so I guess we are stuck for a while with the current setup...unless you can part with the 5-10 grand it would take for custom gears, shafts, bearings, pins, syncros, casing etc. to make a custom setup...