The conditions an instrument lives in or are exposed to can certainly change it or damage it. It's more likely to happen from swelling or shrinking of the top than the neck though. That said, there are plenty of instruments out there without truss rods doing just fine. Deering Goodtime banjos, for instance. I've never owned the 5 string version of one of those, but I have owned two different tenors at various times. One was a 17 fret, the other was the 19 fret version (I think that's right.) Either way, one had about the same scale length as a baritone uke. I'm guessing the string tension was even greater on those necks with steel strings. Actually I'm sure it was, because I tuned mine in DGBE with steel strings. I'm sure that the species of wood used, how it was seasoned/dried etc. plays a big role in any future problems. I know there's not as much care taken with proper wood conditioning before the Asian made mass produced ukes go out.
I've also heard of classical guitars that use no truss rod. I do realize some of those have a rod in the neck that is non-adjustable, but plenty of instruments have no truss rod. The Martin Backpacker guitars also have no truss rod and they usually hold up incredibly well. Of course, those necks are really thick.
I saw your other thread about your buzzing problem. Normally, if it's an open string it is a nut problem...you said you tried putting something in the slot already. Hm. It could be that the angle of the slot is wrong. If you're right handed and have the uke in playing position, try pushing down that B string (just to get some extra break angle/pressure on it) to the left of the nut (on the headstock side of things), and pluck that string while doing so to see if it still buzzes when played open. If not, it may be an angle issue or at least some slot issue. Make sure the nut slot is clean as well....and that the string isn't so much smaller than the width of that slot that it's moving back and forth and hitting against one side.
If you didn't try changing strings, you could try that too. Some buzzes are just hard to track down. Hopefully it's not a loose brace or something that the B string is setting off.
I hope you get it figured out.