Regardless lets check the potential outcomes:
1. Current: yes, else there will be gathering of charge in the cross-segments
2. Current thickness: no, coz cross-area is evolving
3. Float Speed: No, coz I=neAvd and as A builds vd must reduction to keep I consistent
4. Electric Field: No, Is a vector and if the wire has non uniform cross-area then it can't stay in one heading
5. Electric Field Magnitude: No, coz vd is relative to E and if vd is not consistent then E can't be