Several threads on this already... for me a "putt" is anytime I'm using a putting stance/motion with the intent of putting the disc in the basket.
You can absolutely finish a hole without putting.
For the purpose of testing a "falling putt", that's true.
But there are times when I'm out around 30' with howling wind or a serious drop-off behind the basket, or whatever... the conditions are not favorable to make a run at the basket. I will intentionally lay-up as close to under the basket as I can for a drop-in putt. In those situations I don't count (for DGCR Scorebook purposes) that lay-up shot as a putt since my intent is not to put the disc in the basket, just get it close.