I'm sure it could be painted, but whether it's advisable is a different story. How you painted it and what kind of paint you used would have varying effects on altering the stock units absorption characteristics. A heavy coat of acrylic paint would completely alter the absorption and reflection of the acoustic cloth covering the 244. You'd probably render the unit near useless if you completely covered the cloth with a paint the viscosity of interior latex. A carefully applied minimal and wispy "dry brush" painting done like a Chinese or Japanese sumi ink drawing using an artists acrylic paint would probably have minimal effect (it would have to just sit on the top surface of the cloth and not penetrate it deeply.) If you removed the cloth and painted it with a highly diluted acrylic that behaved more like a watercolor, you'd alter the absorption/reflection to some degree. How much alteration would depend on how much paint remained in the fabric after it dried.
I'd never chance it myself. If I wanted to have wall art combined with the traps, I'd just start over again with digitally printed versions. Then you know they'd be working correctly as intended.