NO!
I only allow them to perch out there while IM OUT THERE and the whole family found this rediculous because its a HUGE screened area... whats going to happen? They cant go anywhere!
I be damned! My Peaches was spooked today by the lawn man and fled the stand... you already know where this is going...
She landed straight in the pool. Baby, trying to help here soon followed

As I got the both out (rinsed them well) I noticed that they were staying above water by spanning their wings but I assure you... they couldnt have done this for very long.
IF YOU HAVE A LANIA AND A POOL DO NOT LEAVE YOUR BIRDS PERCHED UNATTENTED. HAD I NOT BEEN OUT THERE BOTH OF MY BIRDS WOULD HAVE BEEN FOUND DEAD.
I would imagine, correct me if Im wrong, that this would apply to toilets as well. Mine will now stay closed. A clipped bird CAN fly... all it needs is a spook.
Not preaching, just sharing my experience before it becomes yours.