No carbs no insulin

As you say, it depends.
Not only on your current BG level (which you would definitely need to correct with insulin if it is too high) but many people find protein causes spikes in BG if they eat no carbs.
The "protein effective" is different person to person so the best thing is to eat and test.

...and if you are on a basal - bolus regime, you still need your basal insulin regardless of how many carbs you eat, or don't eat.

I wouldn't inject for a carb free meal, but would still monitor and should my levels have risen due to protein, treat it as a correction and dose accordingly.

Defo no carbs no jabs for me as well. But I would monitor my bloods after for a while. Luckily I have the Libre so easy for me to check