I used to think yes.
Now, I am not so sure anymore. A typical flourescent bulb does emit UVA & UVB spectrums of light but they also follow a sort of inverse square law in that their intensity drops signifigantly over distance.
A high powered linear tube for a reptile cage has a penetration depth of 20" max and that is a bulb designed to maximize UVA & UVB output. Toss things like screens and diffusers in the path of the light and the the intensity of the spectrum is damned near killed. IIRC, UVA&UVB cannot pass through plastic/glass very well at the levels that linear tubes produce.
No matter what, it doesn;t hurt to wrapo a towel or t-shirt over it to be safe.