I've gotten conflicting reports as to the nature of Tru-Oil. Some say that it is a mix of varnish and oil, while others claim it's linseed oil that has been heated in the absence of air to polymerize it. I rather incline toward the latter explanation at present.
Martin Schleske did a study, reported in the 'Journal' of the Catgut Acoustical Society in Nov. of '98, comparing the effects of various finishes, including drying oils and oil-resin varnishes. He found that straight linseed oil on wood added mass and damping, but did not provide a good water proof film over the long term. Linseed oil has fractions of different molecular weight, and the lightest ones can penetrate deeply into the wood before they harden, so it tends to add a lot more mass than something that forms a film on the surface. All of the finishes that had il in them, even the cooked oil-resin varnishes, added damping, more or less in proportion to the fraction of oil in their makeup; so 'long oil' or 'spar' varnishes added more damping than 'short oil' , 'rubbing' varnishes.
I'm pretty sure it was Mayer in his 'Artist's Handbook of Materials and Methods' who pointed out that linseed oil never really stops reacting with oxygen, shrinking and getting harder as it does so. Over time a coating of oil can actually cause canvas to 'rot', tearing it up as it shrinks. This necessitates the common restoration practice of 're-lining' a painting: stripping the old canvas off the back of the paint layer and putting a new canvas on.
I'll note that none of this directly addresses the long-term effects of Tru-oil. If I was more sure of what the stuff is I'd be more sure of that. If, as I suspect, it's a polymerized linseed oil, then it would have few, if any, low molecular weight fractions, and should not penetrate deeply. That would limit the added mass and damping. It's possible that Tru-oil does produce a water proof (rather than merely water repellant) film. I note that, as a gun stock finish, it's meant to be re-applied periodically, which would renew it's water repelling ability. I have used Tru-oil as a neck finish when so requested, but I avoid putting it on tops. I suppose the whole thing could be settled if we just asked Sherwood-Casey what it is...
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