If TLV61220 Vin > Vout

No issue. but the VOUT will be higher than the setting regulation voltage.
what is the VIN, and VOUT value

Vin is bettery voltage 3.2V to 4.2V, Vout is 3.3V

VOUT is approx. 3.6V if VIN=4.2V
if you need VOUT=3.3V even when VIN=4.2V, a buck-boost converter should be used,; or can accept VOUT higher than 3.3V at high VIN condition?

what is the output current?

What happens when Vin = Vout? In my case Vin comes from a pair of AA alkaline batteries, which can start out at 1.6V each, (as noted by DN 019) so Vin starts at 3.2V, and may drop to 1.6V as the batteries discharge. Vout = 3.0V. With Vin < Vout, there won't be a problem, but what happens with Vin between 3.0 and 3.2V? How does that affect power supply efficiency? Will this generate extra switching noise?

Hi Emil
the device keeps switching at VIN=3.2V, and VOUT=3V condition. it don't affect the efficiency, but the output ripple would reach 200mV
refer to following link
e2e.ti.com/.../1179.tps61220-performance-with-vin-near-vout