The Win 94 had a lever activated safety, you had to squeeze it in to get a shot off. Does the Marlin?
As for negotiating brush so heavy it would snag a firearms parts, that's up to the user to assess as a risk. CCW discussions involve holsters swiping off safeties - or not - same for rifles in the field. If the firearm can't be safe in the users hands traversing rough terrain, it's time to reconsider one that can be.
It's also on the user - with that ear plug in place, will the firearm go off if the hammer is pulled back and the trigger released? Has it actually been tested at the range? It would then go to how the trigger got released while being carried in heavy brush - and it needs more protection.
If things are that rugged, then carrying on an empty chamber and cycling the action as needed would be one answer. It would seem safer than trusting a soft polymer bit of foam that could be lost at the wrong time.
There's another issue, too - how does one negotiate brush so heavy it is in contact with the shooter, and do so quietly? The noise can and does alarm game. To then consider that there would be a need for an instant shot from a loaded firearm sounds as if the behavior and tactics aren't matching the purpose needed, to silently stalk game to keep them unaware.
Much of all that could be said of any rifle or pistol used and tactics in the field.
So, if the point is to block the hammer from falling because it's seen to be too unsafe because of the conditions, then maybe it's too unsafe for that firearm in those conditions. Don't do it.