Can I connect 2.7V to VDD and 3.3V to VLOGIC? In general, can VLOGIC be higher than VDD?
It is advisable to keep VLOGIC lower than VDD. You can confirm this be diode checking VLOGIC with respect to VDD.
What does this mean?
"You can confirm this be diode checking VLOGIC with respect to VDD."
Set your DMM to diode test mode then connect the positive probe tip to the VLOGIC and negative probe tip to VDD. Should be able to measure a diode drop (approx 0.3) if there is an internal diode across VLOGIC and VDD.