I do believe that the Gen has more base hp than his bodyguards. Besides from countless experiences of even a vanilla general being the sole survivor of his unit, it makes sense from a game balance perspective to prevent every battle from degenerating into a "who can kill the enemy general with the first missile volley" contest.
I tested a custom battle a few times using my General vs 3 Scots Pike Militia, AI put 2 in long spearwall with their captain in back. I charged the enemy's left (my right) unit so my general would land on pikes instead of around the edge of their formation. With bodyguards in 2x10 formation, over half the front row usually died on impact, but never the general, presumably because he has more hp. Using Scot Noble Pikemen instead of militia version, my general usually died on impact along with most of the guards. This seems to support that the militia could kill the guards on impact but not the general because of his higher hp, instead of some weird "the general himself doesn't have a lance so isn't actually charging onto the pikes" type thing going on.

I have also observed in-campaign AI general (with maybe an extra hp or 2 but nothing special) defending his town square and surviving massive amounts of arrows being fired directly at him after the rest of his guard shrugged off only a few arrows each instead of 50 before dying.