Will a coil of wire acting as an antenna improve reception/transmittance?
I thought that a coil of wire might be good as an antenna.


There are a lot of antennas that could be described as "a coil of wire", and some of them are pretty good, but there's a lot more to antenna design than just randomly coiling wires.


  If this is valid would using said antenna improve reception and transmittance if used? 


As opposed to no antenna at all -- maybe.  If the size of the coil is closer to the wavelength of your signal than the antenna terminals on your radio, then probably.  As opposed to an optimal antenna -- no, pretty much by the definition of "optimal".


  Would an antenna of this kind be stronger with more turns in its winding?


Only if it didn't have enough turns to begin with.  If it already had enough, or too many, then no.