Cath's joining situation is actually about as good as it gets for an underleveled dood. It's even better than Chad's on hard mode. In Chad's joining chapter, soldiers can kill him in one hit, and he can even miss them since his hit on them is only about 80, so even trying to finish off a weakened soldier can be fatal. Other than soldiers, there isn't much except cavaliers, half of which he may or may not have enough atk to even do damage to. They don't kill him in one hit, though.
Cath joins in a chapter full of steel/hand axe fighters that have lol hit, and she gets HM bonuses, so her chance of getting hit is pretty low. Though she does die in one hit if she happens to get hit, until she reaches a few levels. With the massive growths thieves have in this game, that doesn't take long. The fact that she's a thief also adds to the exp gaining. She starts out gaining ~70 exp per kill and is still gaining almost 50 per kill after gaining 10 levels.
The next chapter has more steel axes, but it also has lots of use for a thief (loads of chests and FoW), and you have to split up to get all the chests in a reasonable amount of time, so you have reason to deploy her even if you're already using Chad. You can get in some levels while getting chests.
After about 6-7 kills, she's pretty safe on her own since she doesn't die in one hit and has about a 2% chance of getting hit. So I think she's pretty well off. If you want to level her up, it's very easy to do so.
It's too bad her supports suck, and thieves don't promote. Otherwise she could actually be good.