Hi is it possible to copy something in photoshop and paste it into illustrator and maintain the transparency instead of having a white background?
Use the Library panel (Available in CC). The library panel deals with transferring artwork between Adobe programs much better than copy/paste drag/drop.
In Photoshop drag your artwork to the Library panel. (Window -> Libraries)
In Illustrator drag the artwork from your libraries panel to your artboard. (Window -> Libraries)