This may be true in practice, but is actually not true in theory, provided that level drain attacks are functional (they aren't in BT3 DOS, for example).

Assuming that level is 16-bit:
A bard can level up past level 2000. At that point, you can expect to have 5-digit HP, even if you started with low CON. If that is not enough HP, you can get more by intentionally getting level drained; when you are level drained, you do not lose any HP, and you can regain the level as normal and get more HP. Repeat until HP overflows.

If level is 8-bit (is it in any port?):
Once you reach level 255, leveling up again will set your level to 0. At this point, you can keep leveling up, no more XP needed. Repeat until HP overflows.

Even in practice (where we're not leveling up into the triple digits), the fact that XP requirements stop increasing past level 13, and that the level cap is high enough that you aren't going to reach it in practice, means that, if a character's HP is too low, that can always be fixed by leveling up. This isn't like many other games where levels get harder to gain without limit, or where there's realistically a point where you *can't* level up any more.

(I could also note that, in BT1 and BT2, when you're past level 100, your stats will be maxed out for sure, and in BT3 (unless you're playing the buggy DOS (or Amiga?) version and horribly unlucky), you can expect to have maxed stats well before level 200.)

Edit: Actually, it looks like my calculation was off by an order of magnitude; a Bard can pass level 20,000 before hitting the limit of 32-bit XP. At this point, HP will overflow before the Bard's level maxes out.