It will if you get it on the shrubs.
It's absorbed by the leaves (and presumably stems) of the plant and absorbed into the plant's system, whereby it interferes with the growth, and a couple of weeks later the plant wilts and dies. It becomes inactive in contact with soil. Therefore, if you make up a solution of glyphosate and apply it carefully to the sorrel (eg using a paintbrush) avoiding your shrubs, then it will kill the sorrel and not the shrubs.

Once your shrubs are large enough to be covering all that bare soil you'll have much less trouble. Sorrel apparently likes disturbed ground, which is an indication that it's not too happy about competition from other plants and about shade (and so it responds by getting in early on to ground that's recently disturbed and therefore without vegetation).