Yes , its possible and pretty simple , you can flood coat with screen inks or just spray paint it. You need to clean it first and use an ionizer on it to remove static.(or some other static removal method) Cleaning is BEST accomplished with warm soapy water. Static is a problem with acrylic , it will attract any dust which will mar the paint finish.
Clear acrylics can be sprayed from behind and the lasered or engraved.
There is one BIG caveat to all this , sawing , milling , bending , heatforming and lasering put HUGE stress into the acrylic , espcially extruded stuff. Using paints with solvents can lead to problems if any of these have been done prior to painting as the solvents induce stress cracks and or crazing which get worse over time. Same applies to cleaning it , solvent are not recommended.