Pruning a Tea Rose

Do we deadhead the Niles Cochet or not? This was a lively discussion today in the garden. 

Five, Seven, and Two discussing their predicament.
Alice's Adventures in Wonderland

Here's how the Niles Cochet flowers grow:

A single rose on a branch

Notice the multiple buds from the base.
Will the rose fall off by itself eventually once these buds grow?

Hard to say.
Will have to check in spring.

Now what?
Will one of these branches form multiple bud and the other stems fall off?

The Niles Cochet, if given the space will turn into a classic big beautiful rose bush blooming and blooming and blooming.

Here's ours which has over time been rudely pruned:

References

"Pruning Teas My Way", Cass Bernstein, Deadheading is optional and best done by snapping off spent blooms. Do not shorten canes...just to shorten canes." She also says you can leave teas for decades without pruning. She says "Teas are not among the classes of roses that requires the stimulation of pruning to perform at their best. ...The objectives of pruning are removal of diseased or damaged canes; removal of canes that are "used up" because they have few viable active bud eyes; and removal of small, twiggy, old or dead growth that interferes with the plant's active growth patterns. Mature Teas can tolerate more pruning as the need arises, especially to channel new growth into young, vigorous canes by removing dead-end growth."