Short answer: probably not.
Hibiscus are full sun plants generally and they don't tend to thrive in cages.
That said, I kept hibiscus in my Veiled's cages for years. He loved to chomp on the leaves.
The real trick is to have more than one hibiscus and to rotate them in the cage. Inside for 3-6 months, outside for 3-6 months.
They need a reasonably large pot if they're going to get really bushy and flowery, so make sure the base of your cage can support it.
I had a big cage so I supplemented the light from the spot bulb and UVB fluorescent with about 8 regular CFL bulbs (about 15W-20W each, alternating warm white and cool white).
If I did it again I'd probably use those grow-light LED strips for the supplemental lights.
Either way, you're probably still going to have to rotate them out into sunlight for optimum health.