I would be careful of how you use the word timbre, which refers to the quality of the sound.
There are several embedded questions here, and I will try to address them.
Most doubling rules apply to voice-leading, and the treatment of the bass is integral into creating a satisfactory and refined sound. Instead of "accent" I would use the word "emphasize" which is a subtle difference.
Bass register very typically serves as the aural foundation. So, whatever note is put in the bass, the other notes will be heard in reference to the lowest pitch, regardless of whether or not they are functional, and regardless of whether or not you want them to be; it's just the way things work.
It is impossible to discuss harmonic function without understanding contextual harmonic motion. I want to clarify for other readers that "C5" refers to a specific guitar chord-shape. With a "D" in the bass, it wouldn't be heard as a suspension unless there was an anticipation in the bass, followed by the actual suspension, and then resolved by downward motion to a resolution. Downward basslines are very popular, though not usually achieved through suspension and resolution.
Bass is your stability, and to suspend it would be to suspend your foundation, which creates a certain effect.
Your question of whether or not it works is subjective - it depends on what you're trying to do. If you're trying to destabilize your bass and blur harmonic function, then yes, it would work. Otherwise, it just sounds like a Dm11 with some omitted notes.