Borrowing from Arabic قِرْطَاس (qirṭās).
karatasi (n class, plural karatasi)
1) paper (material for writing on)
Yes, it could. Nouns in the N- class don't in general have a plural. I think there are some exceptions. If you want to specify whether you need just one or several pieces of paper you do that by changing the verb. Besides conjugating for the subject, the verb can also take an object concord marker. For this case you could write "Ninaihitaji karatasi" for the singular and "Ninazihitaji karatasi" for the plural.
Besides, if you want to specify that you need exactly one piece of paper, instead of just some unspecified amount of paper, I would probably say "Ninahitaji karatasi moja", for "I need one paper", instead of just "Ninahitaji karatasi".
But, back to the question. I think you can translate karatasi as both 'paper' and 'papers'.
Karatasi is in the n-class.
So, yeah. You can use 'I need papers'.