Maybe. I had a situation that suggested this isn't always true. Long story made short: Panicked diver, hyperventilating and as a result feeling woozy. Out of abundance of caution, I put her on oxygen.
A DM from another shop assisted and grabbed the kit from my truck (I'm close with these folks and we routinely help each other out). I started rigging the demand valve and was preparing to hand it to my diver while the DM turned the air on. Once she had the tank valve on, she immediately turned on the oxygen flow to the non-demand side and asked if she should set it to 8 cfm. Yeah, no. It's the demand valve in use, so the non-demand should be left off. And 8 cfm isn't, if I recall correctly, something that'd routinely be used. I'm guessing that particular DM had never encountered deployed an oxygen unit in earnest and was a little flustered, but it didn't just come back to her....