In a congested network, yes, UDP will send its packets faster than TCP, this is because TCP takes then congestion into account using a mechanism called congestion control. UDP has no congestion control, so it'll send packets as fast as the local network interface will allow.
So if your first priority is to send the packets, then UDP is the way to go. However if you're also interested in receiving them, that's another matter. Sending UDP packets into a congested network at a high rate will cause it to become only (much) more congested. This will inevitably lead to long delays and packet loss.
The problem here is not TCP nor UDP - but the congested network. If the road is congested, it doesn't matter if you're driving a car or a bus, you'll be late either way.
It doesn't matter all that much which protocol you choose. To send something quickly over a congested network, you need a solution at the network level, possibly some QoS mechanism. QoS can give you the network equivalent of bus lanes, that allow buses to quickly pass congested roads.