This really depends on how you play the trackball, the quality of lip around the ball, and how worn the rollers are. Some other stuff like weight of the ball, too, I guess.
If you just hit the top of ball with your palm (coughgolfgamescough), no need to worry.
OTOH, if you play with your finger tips and ride the ball all the way to the CP top, look out. Here's where the lip and rollers come into play. Pinched fingers are not fun.
IMO, happs/atari (normal & high lip) have a slightly better lip than betson, which is slightly better than wico's (I'll talking 3"), AFA finger pinches. My wico 2 1/4" seems to be the worst, but happs 3" high ball is almost as bad. If you put plexi/lexan over the TB, you also have to check it's quality.
Now, I'm talking about my fairly new trackballs, and as mentioned before, worn rollers drop the ball lower, increasing the size of the gap between the ball and the lip. So bad rollers = more pinches.
You might want to take note that heavier and sticker balls can pinch harder, AWA faster moving balls. Also note I don't have any plexi coming close to my TBs, so AFA plexi goes I'm going on what others say.
AFA getting a finger actually stuck inside instead just the skin pinched, unless you have a really bad plexi-trackball match or totally worn rollers, and baby size fingers: don't worry. You'll only get pinches.
my 2 cents.