It is never safe to put solvents of this nature into a carpet cleaner. Solvents are flammable, the fumes of which can be set off by the motor of the carpet cleaner. Solvents also won’t mix with water and can damage the plastics that your machine is made from.
You’re going to have to carefully spot clean the paint from the carpet by hand. Test whatever solvent you use in an inconspicuous area to make sure that it does not damage or discolor the carpet. Use care not to over saturate the carpet with the solvent.
Once the paint has been manually removed, follow up with using a carpet cleaner and carpet-specific cleaning solutions. The Rug Doctor Mighty Pro would be the best choice, as it is powerful enough to deep clean and extract the solvent residues.