Installation and removal of previously install non norton product

If I am replacing Mcafee with norton--when the norton cd is placed in pc it will alert that there is another antivirus on the pc and ask permission to remove it.  Two questions: (1)  during the time norton is uninstalling mcafee and checking for updates--won't my pc be exposed? (2) after norton has removed mcafee , if I run the mcafee removal tool to be sure all traces of mcafee are off my pc would running that tool cause any problems to newly installed norton?