No. The Nintendo e-Reader peripheral connects exclusively to the original Game Boy Advance (model AGB-001) via its external link port.
The Game Boy Advance SP (AGS-001) lacks this port; its link port is internal and shaped differently for the SP link cable. The e-Reader physically cannot attach to an SP, and the SP firmware does not support the device.
To use e-Reader cards (e.g., for Animal Crossing, Pokémon, Super Mario Advance 4), you must use an original GBA or a Game Boy Player on GameCube.