I've previously discussed this topic in articles before.
This is called "latent variables".
Essentially latent variables are things that impact the results but cannot be measured.
These are your "useful" intangibles:
* Hits and physicality leads to more tentative play or increase in chance of injury on opponents
* Leadership causes cohesiveness in following system
* Character in the room improves morale and effort
* etc.
All those factors should in theory lead to improvements in the measurable: shots and goals and wins.
(I have to say though that I am extremely skeptical on your fight argument, both in injury protect and booster. There is a lot of counter evidence.
Injuries: While not causation, there is a relationship in those that carry fighters tend to have more non-fighters injured and also lose more games.
Morale/Energy boost: Shot and goal rates do not change after a fight more than we expect given that the ones usually fighting are 4th liners with the worst shot rates and the new players are usually rested top line players with high rates.)
I've gone into this pretty deep at both AIH, JN, and HG, so I won't too much. You can search Google for past articles I've written on the subject.
The danger with specific instances like this, is you are taking a player that is both visibly and measurably deficient in events that directly lead to goals and wins because he of areas that could be indirectly beneficial.
The issue with the immeasurable is that you can't measure it.
Is the player actually helping out there?
Does it actually eventually lead into making up for where they hurting?
It seems intuitive that it helps, and if you are to choose those players, fourth line role is the best place. Fourth line players can be sheltered, not just in terms of usage, but also the minutes they see. Fourth line players do not just see minimal minutes, but they tend to play very low leverage minutes as well (large leads or far behind, not last few mins in period or game, special teams, etc.).
So, if positive latent variables were to make up for negative on-ice variables, this would be the place.
However, the issue with this is that just because something seems intuitive, it doesn't necessarily work out in the order of importance that one would assume.
For example, we see this in face offs. Face offs matter, but not nearly to the degree that many would, and used to, think. The second worst team in FOs was the Canucks last year. The very high-end of estimate would be that it cost them 7 goals last season in their differential, maybe 3 points. Even then that can be an over assumption. We look deeper and we see most of the losses came from the Sedin line, who actually out shot and chanced opponents when looking right after a FO. FO is only just a means, the end is puck control to lead into shots and goals.
Many latent variables are a means to an end as well. We know Peluso hurts in shots and goals, even for a fourth line player. We do not know whether his latent variables make up for that. We also don't know about other latent or indirect variables that could be impacting things as well (random ex: Petan taking more time keeping top lines fresh for high leverage mins). It's not like the alternative options, who would be better in the measurable, have no chance at being also better in the latent variables too. There's also possibility of negative latent variables in having players more likely to have shots and goals against, as no one likes losing.
You are trading some known hurt for some unknown help. It can be dangerous. No one really knows if it is right or wrong, but I'm wary.
No matter what, I do not like the fact that the Jets have essentially carried a bottom 5 fourth line in the league for years in the measurable results.