If you're on top of an OS, I can't say (depends on the OS)... but reading the switch is the responsibility of the reader, not the card. The card has no idea if it's write-protected (by the switch mechanism) or not. [1]
Just using the same SPI operations you always use for write should work fine. There's not even a lock-status register or anything to check/clear first for the switch mechanism.
Perhaps it's not within the capabilities provided by the OS or the driver, because they're "well behaved", but the position of the switch is in essence a boolean sent to the host device and not a barrier to electrical signals that would write data.