Yes, it is.

The register is not exactly the same though, the english sentence is pretty formal while the French one is more familiar. It wouldn’t fit on a sign for example, it’s more common in spoken French.

On peut faire ses devoirs à la bibliothèque.

is fine and neither formal nor particularly colloquial.

“On” matches “one” here (indefinite pronoun).

Doing homework in the library is allowed.

This sentence shouldn’t be confused with:

On peut faire nos devoirs à la bibliothèque.

which is standard spoken French for:

Nous pouvons faire nos devoirs à la bibliothèque.

i.e.:

We can do our homework in the library.