I have no experience with guitar tuners but here is what Jobst Brandt has to say about them. There are also spoke tuning phone apps available which would eliminate having to take a separate guitar tuner when touring.
Jobst Brandt explains...
The frequency of a plucked spoke depends on its cross sectional diameter, its length, its tension and the adjacent spoke and where it intersects this spoke. Interleaved spokes, therefore, have a complex tone that has multiple modes, the primary mode not containing the most energy but rather a mode that resonates in the free span of the spoke. Seen on an oscilloscope, the spectrum is dirty and not repeatable. Using tone by exciting the higher modes of the spoke is useful for balancing tension but practically useless to gauge absolute tension. By plucking spokes near the nipple, the higher modes are excited which largely avoids the problem of interleaved spokes. The musically adept human ear readily recognizes the "quality" of the tone that is otherwise difficult to define analytically.