I wouldn't bother doing this with a 10 gal. I did cut out the center braces on my 75gal and 40 gal oceanics, because the center braces on these tanks are huge, and block light. I didn't leave it unbraced though, I went back in and put 3" strips of 3/8" glass all the way around the 75, basically creating a eurobrace. I only put 2 strips of the same size glass on the 40.
What's your reason for wanting to do this on a 10? I think it would probably be fine, I've seen more than one home made tank that was in the 10-15 gal range that didn't have the plastic bracing, but most of them were custom made with thicker glass than the normal 10gal tanks.
B