I have seriously considered doing this with my cheap uke from tiem to time. I highly doubt it'd ruin the sound, but there are a couple things to keep in mind: 1) it will ruin whatever finish you have on the uke, 2) any burning you do will be permenant, so I woudl only burn something on a cheap uke unless you're really goot at woodburning and know you want the design in your uke forever
...and now I'm reconsidering burning something into my uke... I'l let oyu know if I do anything. If I o anything, it'd probably just be some accenting around the soundhole or the edge of the soundboard.... maybe something on the headstock.