Yes, I have driven t post with my fel. if your ground is not to hard or rockey, push a little at a time. If you try to go to far to fast, it may bend or not go in strait. it takes 2 peopel to get it strated on to hold the post the other to work the loader
They do it all the time here. Just have to have someone to make sure it's straight when you start and push it in and let off and move the tractor a tad if it's springs out of position. They use the channel on the bottom of the bale spear to push them in with. I wouldn't try with the bottom of a bucket unless you're good enough with a loader that you can keep a bucket level as you're pushing in.
My wife and I have used our FEL to install 200 or so. We have clay with some rocks. I have bent a few over the years, but not too many. Our Bobcat worked well. The loader was fast enough that you could smack them a little, instead of just pushing. After starting she would move well out of the way.
You do need to use care.
Kubota MX5100F IH McCormick Farmall 140, Massey Ferguson 135
It works better when the ground has some moisture in it. Around here the ground gets mighty hard in July and August. We've done many. Go slow and make sure your helper moves back.
Put a dozen or so in with the FEL recently. I was by myself and noticed some missing or knocked over. I got them started a bit by just muscle and when they would stand by themselves, I would get on the tractor and finish the job. I didn't bend any, but did push a few deeper than I wanted...