No, it won't. You've not mentioned what version of 1.9 you have. Along about version 1.9.6 Moodle began to salt passwords ... check your 1.9 config.php file for a salt line.
So since installing a fresh 2.x, the fresh 2.x will have a different salt and thus the old passwords ... even the password you see in a mysqldump of user info (password included) ... wouldn't work on the newly installed 2.x.
One would have to add the salt line from config.php to the config.php file of the new site if one used a 'doctored' mysqldump formatted as a csv file for that to have a chance.
A lot of trouble if you ask me ... besides, restoring your 1.9.x courses to a 2.x won't bring across users that were enrolled anyway.
The only way to get it all (courses/users with passwords, etc) from a 1.9.x is to migrate the site upwards through a progression 1.9.x to 2.2.x to 2.3.x to 2.4.x (and to add to the confusion ... 2.5 just released).
'spirit of sharing', Ken