Almost certainly NOT!
In spite of all you hear. Flute players are being told a pack of lies. Every time a reasonably scientific comparison is made, the results tend to show that material matters very little, but player and flute DESIGN matter enormously.
For one such research, see (at least the summary) at
http://iwk.mdw.ac.at/Forschung/english/linortner/linortner_e.htm
However, the human mind is very easily deceived, and if you BELIEVE that diamonds on your flute crown, or precious metal this and that, will improve your flute playing, then they almost certainly will, especially if you have paid megabucks for this belief!
Remember, flute makers are out primarily to make a buck from sales, and they construct associated advertising to encourage sales. Advertising very seldom tells the truth.