Can I use "verbally" to refer to textual communication? For example, can I say "Verbally encourage this behavior" meaning "Encourage this behavior in writing"?
It would be unwise.
I suspect most people might understand verbally to mean orally, while those with a more classical education might understand verbally to mean with words from the Latin verbum as opposed to drawing pictures or giving a hug.
So if you mean "in writing", then use that phrase to avoid misunderstanding; literally may also be misunderstood.
This may contrast with other languages. For example in French law, a procès-verbal is a detailed written document.