It makes sense, but it's awkward because of a matter of nuance. When "give away" is used as a verb, generally there's no object given (who/or what receives it). This verb is generally used in context to highlight that the subject is parting with something. To sound more natural in the sentence given, just use "donate" especially if you're writing in an objective style.

It's ok, for informal conversations like with a friend or family member

"We could give money to sick children" is better. This sounds like you are suggesting something to donate to.