Can PV connectors be unplugged while current is flowing?

No. Do not use PV connectors as load-breaking switches. Disconnecting a DC circuit under load can create an electrical arc, with shock, burn, fire and equipment-damage hazards. Stäubli’s instructions require de-energizing before mating or disconnecting, and SolarEdge warns that modules can still produce voltage without a connected load. Qualified personnel must follow the applicable module, connector, inverter and site shutdown, isolation and verification procedures. Stopping the inverter or opening one switch alone is not proof that every conductor is de-energized. Live parts may remain energized after isolation or connector separation. Use the selected product’s instructions and applicable electrical rules, not a generic unplugging sequence.

Sources: Stäubli, MC4/MC4-Evo 2 cable assembly instructions MA294, safety instructions, page 2: https://www.staubli.com/content/dam/ecs/technical-documentation/assembly-instructions/RE/PV_MA294-en.pdf SolarEdge, PV Module Monocrystalline Bi-Facial Module Installation Guide, printed pages 5 and 8: https://knowledge-center.solaredge.com/sites/kc/files/se-pv-module-monocrystalline-bi-facial-module-manual-eng.pdf