Batman Senora used to – he was officially with Ian Williams but he seldom ran anywhere other than France (took on Best Mate and Beefy once, ran at Wetherby too on an occasion).
There’s probably one runner every 10 years but the hurdle races there get a number of Mullins entries so there’s hope yet.
If the Alners, Jim Dreaper etc. knew how much it was worth in comparison to the races they aim their horses at (particularly for British trainers with the exchange rate of the pound at the min) they’d definitely take an interest.