Hello and welcome to Frog Forum

In my experience:
They sure do!
I call mine 'tree frog wannabes'

below- this is 2 inches from the 'ceiling'
http://www.frogforum.net/dart-frogs-...eucomelas.html

see photo #5
They climb all over the back - including scaling the vine they will sit up there for hours
http://www.frogforum.net/members/fly...eucomelas.html

Remember when you start w a ..........24" high tank - after substrate it's about 18"
18" high tank - after substrate it's about 12"
12" high tank - have to use a lot less substrate -- IMO only good for a spare tank ie quarantine/hospital or for tads to grow out

I keep all my PDFs in 24"H exo terra enclosures; even for the tincs and auratus
My tincs seldomly climb, my auratus occasionally climb.

R imitator 'Varadero' --ALWAYS climb ( in fact ---spend more time up in the vines than on the substrate)
P terribilis - often climb- along a ridge on the background and sit on the very top of a lg pc of wood
or will be found in an open substrate area
O pumilio 'black jeans' - always climb around the broms

The higher enclosure gives you plenty of space ( for planting , especially trailing plants ) and opportunities for hides which will make your frogs very happy

I'm sure other members with leucs will chime in.

I believe, if given the opportunity, your leucs will use every inch of vertical space!

Please chime in !
Lynn