Any bag that just attaches to the saddle or just attaches to the post is fine. But when you attach to both the post and the saddle you need to account for the relative motion of the saddle to the post. This means that if you cinch down the bag when off the bike it might have some movement when you get on the saddle and compress the post a bit - this might not be a problem but it might be something that is an issue.
It all really depends on weight and how stable the bag is and if it is attached to both the post and the saddle - it can be fine but with a lot of weight it will mean it can move around when the post is compressed. It will likely come down to testing it out with your specific bag to see how it works. And if you have a bag that is able to be secured to just the post or to the post and a rear rack then you will be all set.