If a router is sending UDP syslog packets over an MPLS WAN at such a rate that 100% of the bandwidth is being used, how much effect will this have on TCP traffic? I'm not sure to what extent backpressure, RED, or ECN are used.
UDP traffic does not perform any congestion avoidance and is, therefore, capable of saturating a connection in a non-recoverable way.
Backpressure routing is a theoretical concept not implemented on any production hardware that I'm aware of and requires coordination of multiple routers akin to a routing protocol.
RED (WRED, actually) is implemented in some gear, including Cisco, but all it does is start dropping packets in a "more fair" way to avoid problems with aggressive windowing. UDP does not respond to dropped packets and does not handle congestion avoidance, nor would it even be aware of congestion.
The same goes for ECN, which also just adds a flag at a point slightly below true saturation, which is supposed to make the session handler behave like it had just dropped a packet, and throttle back the transmission window. Again, UDP doesn't handle congestion avoidance, so it doesn't even make sense for UDP to be subject to ECN (as in, it isn't theoretically possible for UDP in Layer 4 to do this).
If you are transmitting traffic (like Syslog) via UDP that is not bandwidth aware, you will saturate your line with UDP traffic. TCP traffic will then fall back to extremely small TCP window sizes with a high retransmission rate and you will struggle to send much at all through the link.
The proper configuration is to use QoS to hard-limit UDP traffic on the router to some fraction of the available bandwidth, or dynamic QoS to do some more interesting endpoint-weight based QoS to be a bit more flexible.