One way you can do it is:
1. Once your Org Chart is completed, right click on it and select "Save as
Picture...". Save it as an EMF (default) file type.
2. Delete your current org chart from your slide.
3. Click "Insert", "Picture", "From file" and browse to your new picture
file and select it.
4. Right-click on your org chart picture and select "Grouping", "Ungroup".
5. You will get a dialog box asking if you want to convert it, click "Yes".
6. Right-click your object again, select "Grouping" and click "Ungroup.
You now have separate objects that you can animate as normal. Might need to
Group the text and the box behind it to make one object first. There might
be other ways, but this is the method I use. Hope it helps!