Those that said no are wrong.
Those that said yes, but... are correct.
Thost that insist no, build it and ye shall learn.
The yabut, the coil usually does not really have much effect as
its at the high impedance end. The shear bulk of the winder
looks more like a capacitive end plate and electrically lengthens
the wire. Its calculable but varied with frequency and type of
insulation plus the winders diameter.
Net effect, you wind in a little more and its tuned.
I designed such an antenna package, at full length is was bog standard
dipole but slightly shorter dye to the reel (small amount of metal). Wound
up you took off about 3% (give or take, band dependant) for the lump at
the end. The reel served as insulator as well. Worked as expected for
dipole and no measurable difference from a cut to length dipole for the
given frequency.
We use the twist back the wire on itself to shorten and tune antennas.
Then why not a reel?
Allison