Nope.
"Standard Awards offer expanded availability on flights operated by United, United Express and Copa Airlines (including Copa Airlines Colombia). MileagePlus Premier members and eligible United MileagePlus Cardmembers have access to last-seat availability on Standard Awards on United and United Express."
I would think that even if oversold, if they're selling a ticket, you should be able to purchase it with miles. Perhaps the website won't sell it once the number of tickets sold equals the number of seats in the cabin. I would think that you could get an agent to do it for you.