Can a small business, sole proprietorship, deduct the value of pro-bono professional services on Schedule C?

I'm sorry, but no.  An expense that wasn't paid by the business cannot be deducted.

Did you send the invoice for $0?  You can't deduct income you never received.  You will just have less income to be taxed on.  You take the loss by still deducting all your expenses but not your time or labor.