Nope, it will help virtually never.
Most people on this forum, even the experienced people, dont realize one very basic concept in enclosure building: the goal to minimizing vibration is to keep the enclosure's resonant frequency outside the range the speaker mounted in it will be expected to play, and that there are 2 methods to achieve this goal. The first method is mass loading, to move the rez freq below the usable bandwidth the enclosure will be reproducing. The second is stiffening, to raise the rez freq about the freq band. One, or the other, not both. Most people on this forum think utilizing both methods is the only way to get good results.
Most people here will claim we use a dense material like MDF because its heavy (implying it adheres to the first method, mass loading), but then also say the enclosure MUST be braced (employing the second method, stiffening). You DO want to use MDF AND internal bracing, but the density of the wood is not for its mass, but for its pressure rejection/containment properties.
The vast majority of car audio enclosures are built using method #2, stiffening to maintain a (relatively) high rez freq. To properly employ method #1 for a subwoofer application, where the enclosure rez freq must reside below 20hz (or lower), think concrete. Think... lots of concrete. Method #1 is primarity used in home audio, not mobile audio, simply due to weight considerations.
So, knowing this, do you think sticking a little extra weight to the side of your enclosure walls will do much of anything? Virtually nothing. The dominant force keeping those walls from flexing is stiffness, not simply mass. To improve on this principle, if you have a vibration problem, you must stiffen that portion of the box: internal bracing. That being said, almost all enclosures will vibrate at least enough to be perceptible when touched. If you try to improve your box rigidity/stiffness more and more, you will quickly realize the law of diminishing returns is catching up to you. For most enclosures, systems, and situations, 3/4" mdf walls with some basic internal bracing (rods, internal walls, cross-bracing... not just little triangles in the corners), you will get no audible improvement by going nuts with the bracing.