Yes, absolutely, especially if you put the pieces that connect the barriers together. I've used it a lot without the suction cups. It's a great product and very reliable! I even had one for outside and it worked perfectly!
We had also bought a children's play mat, which fitted in quite well. This held the palypen grid in place (the grid surrounded the play mat) and it didn't matter whether the suction cups held. Unfortunately, I can't tell you how it will behave without the appropriate play mat. In any case, we were happy with the combination purchase.