Do not push something with the FEL using wheel power unless you know it's really light/weak. That goes for trees or digging in hard clay/etc. You can really mess up the front loader as there will be no "relief" to kick in. However, you can definitely push stuff over with the hydraulics, because the system will go into relief before any damage is done.
An example -- when clearing a spot for my barn, I pushed over several 6-8" pine trees (live healthy trees with no widowmakers) using the front loader hydraulics. Bucket up high, curled forward, and then lower the bucket. Levers the tree right over like it was a stalk of celery. However, if you did the same thing but drove forward, you could easily bend the loader arms. Same procedure, but one way uses the hydraulics as the brains with a built in relief safety, while the other has zero margin of error.