Is it absolutely essential that I drink all of the bowel prep before I have a colonoscopy?

Yes. Yes so that your colon is clean enough. If you choose not to, the endoscopist may not be able to see everything' could potentially miss a lesion, and with an inadequate prep, i usually recommend that i repeat the scope much sooner than if i was comfortable i could see everything well. E.G repeat in 5 yrs instead of 10.
Drink it all or call. The point of the colonoscopy is to allow the endoscopist to evaluate the colon fully. This can't happen if stool remains in the colon. It's not just the chunky stuff: liquid stool coating the colon lining also makes it very hard to see. So if you are going to bother to go for a colonoscopy, give yourself the best chance for a good exam. If you just can't drink the prep, call your doctor for advice.