Is it possible to record a voice onto the uploaded video using PHP?
No you can't, at least not by just using PHP, because PHP in itself doesn't provide the necessary libraries for recording sound and editing videos.
To actually record video and sound you'll need libraries like ffmpeg (there's a handy extension for PHP) for video editing and SoX for sound installed on your server. You can then access these programmes by using the the exec() function in PHP, for example. The implementation wouldn't be that simple, though.