There's no single definitive answer to that question. It's not 'critical' to use sealant to secure the hood, in the sense that Parker didn't seal hoods with factory-fresh O rings into place. After 50+ years in compression, the o ring might not be in such great shape.
I've read your other thread in the repair forum, where you say "I kind of like the idea of being able to unscrew it without much difficulty". I will say that I have had major trouble getting an O ring type 51 hood apart, where enough shellac was used to migrate to the O ring. It took a tremendous amount of heat and more torque than I like to use to get it to budge.
Much more and I'm sure the connector would have distorted or even sheared.
Your q is one that pops up fairly regularly. The usual answer is 'seal with shellac or rosin based sealant'. There are valid arugments for both. In the specific case of 51 hoods with the O ring design, my answer would be 'a tiny rub of silicone grease on the O ring to help prevent migration, then apply rosin sealant to the first few threads of the connector'.
I say this because rosin sealant releases with far milder heat than shellac (the same pen was easy to open when I changed nib size), with the added benefit of preventing the hood from shifting off-centre without having to torque down the hood too tight against the O ring.
Your pen is a bit of a question mark, because the vacumatic breather tube and rather odd clutch ring business tell us it's been worked on in the past. Other parts could have been swapped around too. Is there a groove in the hood to accomodate the O ring? How about the connector, is there a blank space after the threads for it to sit in?