Do WP_debug notices explain why my site runs so slow?

No, notices by themselves are not a performance issue and generating them typically doesn’t take considerable resources (there are exceptions if you are replacing error handler – I seen it get slow because of larger output volume and conflicts with antivirus). Of course what they do indicate is potential issues with code quality, which is everything but good for robust performance.

You can try plugins such as P3 for easy first look, but I would recommend to look into more generic PHP profilers, such as Xdebug and XHProf for serious troubleshooting.