Yes! Tons of people do it- look up low tech planted aquarium. Just takes some planning. Mine is a 65 gallon planted tank, no CO2. I'm on my phone otherwise I'd add a photo.
nice set up magpie could you tell me what brand ferts you use please and what are the broadleaf plants at the back and what kind are they on the surface also.
I use Seachem Flourish liquid ferts once a week after water changes and Flourish root tabs every month or so.
The broadleaved plants are swords, and the floating plants are Brazilian Pennnywort, which I love!
I have a dual T5 fixture but it was initially too bright for the fish, so I put a strip of small mesh (screen for windows/doors but not metal) on the lid glass where there aren't floating plants to dim it. Works great, and I can move it as needed.
It's an aqueon setup, with:
(1) 36" 39W T5 HO 6000 K Lamp
(1) 36" 39W T5 HO 650 nm Lamp
I'm sure the T8 would have been fine, and it would be easier not to have to worry about using screen to dim the light.