It will be fine with 3/4" glass. Fill it and check middle for bowing with a straight edge.
I picked 1 of those 5 foot 120 gallon tanks awhile ago too. It had no center brace either but was 1/2" glass. it's fine without but ! pulled the trim (top+bottom) of an old 4' 90 gallon and cut a 4' section and 2-6" sections and fit the top of the 120 just in case. Looks stock so I'm happy.
A 1/2" 120 is very heavy but 3/4" glass is just down right ridiculous! lol
P.S. $10 for 2 Tubes of silicone to reseal is a cheap price to pay for peace of mind! Good luck!