A resonant low note on the basses can reinforce the upper partials of a major harmonic, with good and bad results. This is especially true if the bass is playing an open string a little too loudly. What will happen most often is that the major third+2 octaves will sound out strongly. If the composer has written the major third in, then this can actually be an interesting effect. If not, then you have the “Vivaldi Problem” (my term).
I used to listen to an old bargain-quality cassette of Vivaldi on headphones about 30 years ago. In a slow minor movement, there was a moment when the double bassist sounded a bit too loud, while the ensemble was coming to the end of a cadence on a long minor chord. The result was that the minor third was completely wiped out by the major third partial from the bass overtones (see the sample below – the note marked red will sound as a sharp, not a natural, with this phenomenon).
This is one more reason why a bassist will prefer to avoid playing any open strings at all, unless in the case of pizz and harmonics. The tone (not to mention intonation) is too hard to control.