If you have near elements at the top and bottom of your composition at the same distance, then tilting to get one or the other in focus along with the more distant elements will just result in throwing the other one out of focus.
However, if your near foreground (bottom of the scene) is closer than the overhanging branch, you may be able to use a bit of tilt to find an intermediate position for the plane of focus that will give you less focus spread and, subsequently, allow you to use a faster shutter speed or wider aperture and still get everything in focus.
The trick is to set up the camera leveled and in "0-position" and then measure the focus spread between nearest and farthest elements plus the offending overhanging branch (which should fall somewhere between the two extremes). Now, tilt just a bit and make the same measurements. If the focus spread is less, and the overhanging branch still falls between the two extremes, you've made an improvement in the position of the plane of focus.
Continue this process till the overhanging branch focuses at the same distance as the near focus or just a little ways in from it (i.e., between the extremes, but just a bit). Determine the focus spread (which should now be less than when the camera was in "0-position" and use this to find your optimum f-stop. (If you don't know how to do this, then you need to search on that and figure it out).
Good luck,
Doremus Scudder
www.DoremusScudder.com