If you ask the question in exactly that way the answer would be a resounding YES! Of course people in positions of power try to never have anything in writing because most of what they do would be completely unacceptable to the general public. I have also worked for large companies which put in place formal policies to purge all email from servers more than 6 months old. The official reason was to conserve email server storage. The unofficial reason was that a few court cases had subpoenaed email messages for things happening years prior and management was shocked the discovery process actually turned up those emails. If you don’t believe any of that do some Web searches for the Al Gore e-mail scandal and the DNC email scandal.
Most writers and those who wish to be writers tend to ask the question in a different way. “Will it be good enough?” At the beginning of any writing process this is a horrible question to ask. It will chew up precious time and mental resources pulling you further and further away from that which inspired the though in the first place. You should _always_ write it down. Create a random_scenes, snippets or scraps directory where you store those documents to look at later.
If you are a pen and paper type writer then allocate an entire desk drawer to store nothing but those scraps of paper. Don’t try to get away with just a folder or a couple of hanging folders in a drawer with everything else. While you may not put much stock in the concept, having something allocated completely to your cast offs will shift your mindset when opening it. If you open that drawer to put your receipts, bills, contracts, etc. into various folders then you will not have the same mental shift. You cast-offs will simply be another folder in that drawer you rarely look through.
Even your worst hunk of writing, or that snippet which revealed a darker side of you so many years ago, can have a purpose again. It _did_ have a purpose when you wrote it. You needed to get it out. Even if it was a base and politically incorrect thought at the time, something you would be mortified for people to find now, it helped you deal with that train of thought in some way, making you a better person.
If you live long enough, at some point every one of those scraps will find a home, even if it is on a lowly blog post somewhere. They needed to be written because you wrote them. This is not to say people need to be asked to pay for them. Therein lies the difference of the questions. Never ask “Will it be good enough?” at the beginning of your writing process. That question comes later, during editing. Should you write it down? YES!