No, it can be done.
I've finished both games with no losses.
As for the dragon fight - you don't have to kill the dragon, basically. Or, dismiss or put in reserve your wimpy units before fighting him, you can use the knights and cavalry to kill it.
Generally though, use a save game viewer if you want to play no-loss. You WILL need resurrection and ASAP, and in this game it's random where you get it first. (Or, just start with a Paladin). Use units Level 3 and above, they tend not to die that easily. If you have Level 5 units, as resurrection doesn't work there, you need to use the Rage Spirit Reaper's Time Back. Also, funny thing - Orc Shaman's Ghost Axes can heal Black Dragons, so they are an usefuly pairing. Make use of the Rage/Mana orb generator Rage skill too, it is the key of having enough mana at the end of the battle to resurrect your units while you "troll" the last enemy.
And btw, if you want an undead army and want to make a no-loss game - I have done it, using a little mod that gives you an "Animate dead" spell (replacing the useless Last Hero) - that way you can use this chaos magic spell to raise your undead troops the same way as Resurrection works on the living.