Yes, it will gradually seep down to the tree roots. How much harm it will do the trees is hard to say.
I use roundup to kill the weeks and grass growing around an 8-10 foot Youpon Holly (tree form) several times and it died after a few years...??
The recommendation I have is to remove the mulch, dig out all the weeds, put down a weed barrier landscape cloth, and then reapply the mulch...and put a thicker layer of mulch.
I also found that putting down a Pre-emerging Weed and Feed (like Scott's Weed & Feed lawn fertilizer) on your lawn and around your shrubs and trees will prevent weed seeds from germinating without harming the trees or shrubs...they just soak up the nitrogen and other nutrients. I assume you could probably just buy the pre-emergence weed killer separately and just apply that around the tree rings after you have dug out the old weeds and remulched.
....Rich