I have tried at least 5 planted vivarium with drilled drain methods,
5 with LECA/hydroton
and around 40 with eggcrate false bottom...
tells you which one I like the best eh?:P

One bad cons about drilling holes for a drain is the leak potential...and then the tubing.. kinda annoying specially if you have a frog room... then also sometimes the buckets fills up so fast that they start spilling around cause I haven't emptied em... definitely not the only way to go!!! Also, plants who like to wet feet won't like your drain. Another thing is since the drain won't be exactly in the lowest point of the glass, there could still be small water accumulation, which will be logged in your substrate, unless you have LECA or eggcrate false bottom.

LECA is nice, cheap and easy but I definitely like eggcrate better because it's similar to start with, but more versatility. You might have to siphon LECA false bottom at some point but if well sustained, eggcrates never need to be emptied it... it keep the substrat moist from under (not clogged) and evaporates fast enough. and if you want to have a small pond, it's doable with this type of false bottom!
personally, I like to still keep a corner separated from the rest of the vivarium, which I can drop a lil pump in if I want to make a dripwall, plus moving water is better too.
This way the roots won't rot. Actually you can have both types of plants in there as those who likes to keep their feet wet, will just have their roots directly in the water, as they want while those other plants will stay in you moist aerated substrat


So to answer your question, yes literally any type of frogs will actually be better with a false bottom!! go for it!