Yes, you can get the achievement this way.
You can check your progress in the stats page from the main menu, although this will only show your progess in 10 wave chunks. For example, if you manage to complete wave 40, in the stats page you will see 'Wave 31 - 40' with a tick next to it. You can then complete wave 41 to 50 on another play through to get the achievement.
There is, however, a ribbon that you can get for completing wave 1 to 50 in one sitting (this is separate from the achievement, so you can view it as an additional challenge):
- Long Hauler – Completed all 50 waves in one session