Supposing I don't make a conscious effort to build stats...

If I simply keep trying to advance through the game without stopping every so often to level grind, what are the odds that my characters will become strong enough to continue just by means of anything the game throws at me? I've been strong enough to fail to stop the construction of the [[Warship]] but that was because I spent a real long time improving my HP, weapon skills and spell levels.

Oh yeah, I'm playing the NES version. I already established that no effort need go into level grinding in the GBA version, it all just goes up on its own :P

Provided you have the TELE spell to get you out of dungeons if things get hairy then it's certainly doable. It may take a few runs at each dungeon to get through (in my experience something like five or six attempts) but hey, that's part of the charm of FF2. Ball-busting dungeons FTW!

I usually get too bored around the first town when I play the actual ROM, sad, I can't help you...

if magic would only grow faster, then maybe... but it doesn't, so the game ends up being a grindfest. even cheating with the battle menus feels like it takes forever.

I don't think I cheated at all after the gigas cave and I did fine, but I think I put at least some concious thought into leveling up, esp using drain and absorb to gain hp/mp.

The game starts becoming a pain in the Warship.
You're supposed to survive endless Sleep and Paralyze attacks while being unable to use Exit.
And then you open this chest containing a Gigas, and of course you die.
Whatever, you think.
But ten minutes later you're supposed to enter a cave that constantly throws TWO Gigases at you, the very enemy that solo-slaughtered you a short while ago.
After that part, you *will* need Exit, but at least using it is nicer than level-grinding; it feels better exiting a dungeon a few times, because it gives you a "complete" feeling.
Slowly becoming stronger and stronger in the dungeons each time you enter them feels very nice.