This is a complicated question (and, weirdly, I've been unable to find any concrete data on the spillway or normal release capacity of Addicks reservoir).

Dams release water in two general ways: (1) through controlled releases (aka they open the gates) and (2) over spillways. Spillways are designed to be able to release water if the dam fills too fast and overwhelms the ability of the controlled release structure to stay ahead of the rising waters...

I have read that the Addicks Reservoir spillway is at an elevation of 112.5 feet... which means that once the water hits that level (according to USGS it's currently at 103.74 feet), the water will immediately flow out through the spillway.

I've read that Addicks also has five, 8x6 outlet structures. USGS shows that Addicks has 6 control gates, so my info may be outdated. I don't know the capacity of those outlet structures, but if the 8x6 number is right, they are all about 25% open right now. Meaning they may be able to drain up to 16,000 CFS from Addicks... (at this point though, I am just hypothesizing because I don't have any actual hard data as to the capacity of the controlled release structures).