Is it possible (and safe) to mount a 19-inch 4u rack server on a 2-post rack... by only its ears?
Look at the server's manual. If you haven't bought it yet, look online -- there's normally a mounting guide of some sort, and it might have specific instruction for dealing with a two post rack.
Some systems have alternate holes tapped in the sides so you can mount the ears closer to the center of gravity. The system will stick out the front of the rack, but it'll cause less torque.
Other systems have enough of the heavy components far enough forward that they're fine with 2 post mounting with only sticking out a few inches. (basically, you turn the ears around before attaching them).
Another option is to get a shelf rated for the weight, and install that to take the load of the server.
It depends on your system. You need to find and read the racking manual, or contact the vendor.
Only if you don't have any problems replacing it and the systems underneath it after it falls, to borrow the quote from @PHLiGHT . If you're racking other hardware near this server, and you bump this chassis by accident, will it fall and crush your hands or toes? What if it fell partway and bent the rails? What will you do then?
For many rails, the weight is transferred from the server to the rails to the little screws holding it into the rack. With most servers this is fine, because you have two rails and 4 screws per rail. With a two post system, you might be looking at only two screws on each side of the 4U box. That sounds dangerous.
How are the ears attached to the side-rails? Are they attached with nice solid connections, or are they attached with little wimpy screws, or with little sheet-metal flanges?
Yes you can do this, but I wouldn't recommend it. some servers are very heavy and could also do with support at the back. If your server is only a 1U then it's not a good idea because it's likely to bend at the front.
If it's 4U case then there is generally enough strength at the front to support it OK. I've done this before when we didn't have rails.
Trouble is, it's a real pain to get at the server when things go wrong or you just need to pull it out for some reason. They can be very heavy as you know and when you remove the bolts the whole thing either drops or puts its full weight on the server below (which may be supported in the same way.
Get some rails if you can. Or if you can't get these then other option is to get a shelf and make the server sit on the that. At least then you can remove a couple of bolts and slide it out a bit on the shelf. You can even get shelves that slide.