I am flying back from Corfu, Greece to the United States on two seperate tickets. My first ticket is from Corfu to Athens & the second is Athens to the USA. Will I be able to check my bags thru to the USA on my initial departing flight even though it is a seperate ticket?

Probably not. Luggage is unloaded and sent to the airport carousel _base_d on the cessation of the trip on the ticket. Ticket 1 ends in Athens and the luggage checked in in Corfu will be delivered to you in Athens at the airport.

The only thing that could change that would be if you are traveling on the same airline on both trips or if the two airlines you are traveling on have a agreement that would allow ticket 1 & 2 records to reference one another and therefore bypass the luggage drop off in Athens. However, even if that was the case, I would probably rather pick up my luggage and recheck in with the next airline in Athens. Considering how many bags are lost each year, this is the kind of thing that I would avoid. Adding an extra unusual step in baggage handling raises the possibility of something going wrong by a huge margin.