If the update source is reachable via other non-mpls link, it may not help. Depending on what version you run, yu might try vrf aware bgp conditional advertisement,
If your IOS version doesnt support the above feature, the otehr option I can think of is to use Object tracking to track the TE tunnel interface (line protocol) and use the down state as event for EEM applet. Configure the action to execute a CLI to filter all prefixes to your CE.
You may need another EEM script tracking the UP state of track and execute CLI as action to remove teh filter.