Yes, absolutely. I did it on two different trips. The only hard thing is getting through security because it doesn't fold up small enough to fit on the belt. They had us unload it completely, and then they took it through and used the wand to check it out.
We just folded it up while we were in line and carried it through the walkway because they are more cumbersome and more difficult to fold at the last minute.
I loved having it at Disney. That thing is probably the material possesion I have most loved in my entire life. (I'm not one to get attached to things like that, but I really really loved that thing!) I had the Dreamer Design Ditto, just in case you're looking for a recommendation.