Could be, but phrase it in a way that doesn't sound like "Burdened" is that much of a problem. Possibly when the player reaches Burdened level (if not already Burdened from the beginning), just inform them that higher encumbrance levels slow them down somewhat. At Strained is where the 'd'rop hit could be shown -- maybe, if the player has low enough Str to benefit from it, subtly hinting at the advantages, something like this: "You are now Strained. Have you considered 'd'ropping items you don't need? Then again, the benefits of physical exercise can not be overstated..."

I think the quick hints TB is referring to only list the command, e.g. "d to drop" instead of any full sentences.

Added a simple drop hint once your burden level exceeds "burdened". The tutorial already contains some explanations about how burden levels work.