Yes, it will.
Don't waste your time proving it.
So will primer compound.
It is a wet paste when they squeeze it in the primer like toothpaste.
Then it is dried afterward.
Smokeless powder is soluble in either or acetone solvent, and that is what it is wetted / dissolved with during the manufacturing process.
But in simple terms, cellulose fiber is 'nitrated in nitric acid, the boiled in water several times to get all the remaining acid out of it.
Then pressed to get the water out of it.
Then dissolved in an ether/alcohol bath to further dry it and make it into a 'plastic' paste.
Then it is extruded into pellets, granules, or balls, and the remaining solvents dried out of it.
So water is no longer a solvent that will melt or dissolve the resulting nitro-cellulose powder.
All water will do is help keep it from burning from a spark, etc.
My earlier reference to water, was in relation to using a carpet cleaner to wash & suck it out of the OP's rug. It is safer wet then dry.
And water is preferable to oil on your rug!
rc