adobe illustrator - If I import a .psd file with one layer into Ai and then save as .ai file, is this a true vector file?

I've been asked by a friend to create a vector file from a .psd they have given me which only has one layer. I realize a .ai is a vector file by default, but I often see that an image needs traced, outlined, etc... to be a vector file a printer would be able to use. If I simply open the .psd file and save as an .ai, will she have what she needs to send to a printer?

I'm just trying to help out a friend as I have the software! Thank you so much in advance for any help!