First of all, it should be noted that the LDL212 has a maximum dropout voltage of 0.7V.
Although it is not explicitly mentioned in the datasheet, an LDO typically does not turn off when the input voltage falls below Vout+Vdrop. As long as the input voltage is above the limit of UVLO and the LDO enabled, the opamp contained in the LDO will attempt to regulate the output voltage. The conductivity of the PFET controlled for this purpose is increased as the input voltage falls until the dropout voltage is reached. From this point the output voltage will follow the input voltage by the dropot voltage until it has fallen below Vout-Vf, then the scenario mentioned in the first answer applies.
tl;dr: yes, it will track the input, as long as Vin > Vout-Vf.
Good luck!
/Peter