I went ahead and called the Australian Embassy in the United States to see if they could answer my question. The woman at the embassy was EXTREMELY helpful and answered my question. I am posting the answer below so hopefully it will help out others in my situation.

Answer: Yes, you can apply for another visa while your skilled migration visa is being processed. I specifically asked about travelling to Australia on an ETA visa and Work and Holiday Visa (subclass 462). The embassy representative said that I need to be aware of the requests for medicals/police checks that will be requested by the case officer for the skilled migration visa. She also stated that I need to keep my case officer informed of any travel to Australia so that I can be notified to leave the country when a decision is imminent on the skilled migration visa. (She stated that I do not necessarily need to travel back to the USA for this, rather just anywhere outside of Australia).

This is great news for me because I want to do some extended travel around Australia before I (hopefully) get my skilled migration visa approved.


Hope this helps someone!!!