There is a classification for climbing hybrid teas, yes. They are annotated as Cl HT.
An additional note:
It is a very small classification, and many of the roses classed as Cl HT are quite old. This appears to be the most recent one
http://www.helpmefind.com/rose...
This may be because there is another classification just for climbing roses, and any climbing hybrid tea probably has enough different genetic influences to make it easier to justify placing it in the climbing rose section.
