euh, no, it does not work that way : - )
just send the pdf to the printer and tell them to print in the format you want.
if you send only one pdf for a book, they cannot do otherwise than print the first page as the cover, on the "right side".
often, the print shops want one pdf for the front and back cover and one pdf for the content. in that case they will automatically take the first page as the left one. except if they do not print anything on the back of the cover, then it will be the left side again.
but, don't worry, the printer will tell you what they want... or you will have a way to tell them what you want.
normally, if it's a big printshop they will have a form in the web that will tell you exactly which steps to go through.
and if it's a small one, you will be able to talk to them and check that everything is right.
i hope that it's a bit clearer now...