I'm not speaking from direct experience, but rather from general knowledge of how the rifle works and the properties of naked lead bullets. Hopefully someone will drop in later and draw a more experienced picture.
Depending on how soft the lead alloy is, you would have varying degrees of problems from two points. One is the oblique angle the round has to take to chamber. When the bullet hits the feed ramps going out of the magazine, the force on it would cause it to deform. A softer alloy will deform more and you stand a better chance of the bullet deforming too much to work properly in the rifle.
The second problem comes to play if the round makes it into the chamber without deforming too much, and that is of the bullet having to pass the gas port. Since any naked lead alloy is softer than copper jacketing, it would stand a better chance of obturating into the gas port as it passes down the barrel. This would lead to swipes of lead being jammed in the gas port and causing gassing problems (same reason why it's not reccomended to shoot naked lead bullets through a Desert Eagle. The lead jams the gas port in the barrel and the action doesn't cycle).
The first problem is possible to overcome, but the second problem will occur no matter how hard the alloy is. Eventually your rifle wouldn't cycle due to the gas port being plugged.
ETA: I really have to learn to proof the things I write. I lost a whole alphabet of letters writing this.