Nope. A headless bass probably won’t have a dead spot in the usual spot, but the worst dead spot I ever encountered on a bass was the open A string on a headless. The note didn’t last long enough to even get a sense of pitch - it was just a dull thud.
A bass neck has resonances - it’s a bar; it’s resonances depend on the density and stiffness of the materials, along with the geometry - length, cross sectional geometry, etc. If you have a headstock with tuners, it’s a mass load on the end of the bar - that changes the resonances, but it doesn’t create or get rid of any.
Most basses, if you tune your A string lower, at some point, that open string will lose sustain - it’ll become a dead spot. I had a bass I kept in D standard for a while - the subsequent open G was a minor dead spot. When you remove mass from the headstock, that resonance moves up in frequency, sometimes making your open A string a dead spot.
The thing that surprises me about headless basses is that I see gobs of them for sale, yet I haven’t really seen any out in the wild. During the Steinberger era, I saw a fair number of them out and about, but this time around, I just never run into them.