Going completely without a drummer, no, that wouldn't work for very long.
However, I'd love them to explore a bit more of an acoustic side.
This. Their experimental side is great, but doing "drum-less" music is pushing the envelope too far. Although their music is incredibly varied, it is all the time of music where drums and percussion are integral to the sound.
Also, the poll said "with a drummer, which is the exact opposite of the thread title and what you are saying in the thread. I am assuming it was supposed to read "without," so I edited it.
+1. I'm not just sucking up to Bosky, but I agree.
Drumming is an incredibly important side to DT's music. Whether you like him or not, MP was definitely a skilled practitioner of his instrument, which is proved by his ability to stay in a band as complex as DT's for so long.
I like the idea of going acoustic, but that would work for maybe one song...two would be pushing it. The idea of not having a drummer is, in my opinion, not feasible.
So to answer your question, "Should DT go on without a drummer?" is...
um no?