Can I run electrical raceway on a baseboard?
This is fine

Article 388 sets out the usage conditions for non-metallic surface raceways such as yours, and I seriously doubt that being at a baseboard is going to subject your raceway to the "severe physical damage" mentioned in 388.12 point 2.  Considering that it's an exposed application, indoors where temperatures are presumably benign, your raceway is UL listed for power service (to 600V no less), and not subject to any other significant restrictions from Article 388 (definitely not hazard classified or in an elevator hoistway!), you are good to go running 120V power wires through this raceway setup.  One note though: you will want to run individual stranded THHN wires for hot, neutral, and ground in the raceway instead of a NM cable -- NM doesn't go around your average raceway elbow well at all.