No. Glyphosate only has to be absorbed into the system one way or another. It tends not to be absorbed through dry, woody portions of a plant, but can be absorbed through something like a recent cut. It's actually recommended for treating stumps. Some call it a "cut and paint" where it's cut and then spread concentrated with a paintbrush on the recent cut. This instruction is to drill holes and drop concentrate in the holes.
1.Cut it low
Using a handsaw or chainsaw, cut the living stump as close to the ground as possible. The less stump left behind, the faster it will decompose.
2. Drill holes in the stump
Drill holes into the outer ring of the stump, just inside the bark layer—this is the "living" part of the tree. Holes should be 1/4″ wide and at least 1″ deep and should be spaced about 1″ apart.
3. Apply Roundup® concentrate
4. Wait for the stump to die
This application will kill the stump In 2-4 weeks, without causing it to rot.
It binds very tightly to clay soils, so it tends not to affect roots. But some people think it can't get absorbed through roots, when it absolutely can if they're exposed or if the soil is saturated, like with a concentrate poured directly into the soil near roots.
However, there are different versions of Roundup and quite a few no longer use glyphosate. The brand name has transcended its origins as representing a specific chemical.