The inductance might change only a little, but when used in a LC circuit, the quality determines how accurate the LC circuit will oscillate.
The 'quality' factor of a coil is called 'Q factor'.
It has a large influence. I had once an FM transmitter for indoor use, but when I exchanged the coil with a pcb printed coil it got 3km range.
To increase the Q factor, there are many ways to do that: using a gap between the wires; or use flat copper strips;
or gold plated wires; or a little sideways winding; and so on.
In the beginning of the radio, they used all kind of coil windings, like this one : http://museumvictoria.com.au/collections/items/369111/coil-awa-high-frequency-inductance-1914-1920
If you make a coil for a solenoid, it might change the inductance perhaps by 20%, not a big deal.
Every winding will create the same magnetic flux, and all the flux is added. In theory, you get the same force for a solenoid.
The mechanical strength of the coil itself will be less of course. The wires get more stress and might break when wound too tight.
[ADDED] Not gold plated, but silver plated. Thanks russellz.