Apparently it isn’t that hard to survive the 248 damage from upgrading it. 155hp, 92 shielding from self-targeting with wand and Scroll of Challenge halving the damage. (ShPD 2.2.1)
Pricking yourself to level it up from +9 to +10 does 248 damage. You'd need to be level 28 and at full HP to not die with just a Potion of Shielding. I've usually beaten the game before I hit 28. Much easier to use a Scroll of Challenge or a Blessed Ankh and actually get some use out of the +10 Chalice.