I expect it will pick up the seeds yes. Ideally you should overseed a lawn in autumn when you could wait until the new seed is established before giving it a light & higher mowing.
actually, thinking about it, it might not pick it all up - but it will disturb it & you shouldn't really be walking on it - so, if you really must mow see what happens & you could go over it again later in the year or even early next spring.