May 15 2022 Update:
The AFSP (Alien Flight Student Program) has been renamed to Flight Training Security Program (FTSP). ------------------------------------------------------------------
Short answer: Of course yes! The FAA under the Alien Flight Student Program (AFSP) provides international applicants with the chance to obtain a Private Pilot License (PPL). While the candidate has to do the exact procedure as a US national, they also in addition need to get approval from the AFSP for their flight training.
The AOPA has some great resources on the AFSP procedures. For the visa status, AOPA website states:
Part 61 flight schools and independent flight instructors may train a foreign national if that alien is a legal permanent resident or in a work status (H-type visa) with extended stay privileges or a refugee in asylum status with appropriate DHS documentation. They also may train a foreign national on an F-1 (academic visa) provided that the student is still enrolled and attending the college or university as shown on the F-1 and the student has notified SEVIS of the additional training being received at a non-SEVIS approved school.
The procedure is pretty straightforward. AOPA lists the steps here. Here are a few more details to help you with AFSP approval for Pittsburgh/CMU:
Before you start your application please reach out to your OIE person in CMU and let them know. Thankfully, with a few students in CMU already pursuing PPLs, OIE already has some experience with this.
The AFSP portal expects your flight provider (school or individual CFI) to be already on the AFSP portal. In some cases, they might be listed there. In cases they are not, they need to enroll themselves as providers on the AFSP portal. This might take a few weeks depending on the local FAA office.
One critical step is to provide your fingerprints to the AFSP. This can get tricky but Pittsburgh has multiple options. Please explore all the options. You only need to submit fingerprints once. Any future training requests are much faster. Previously, people have had success with IdentoGO.
YOU DO NOT NEED AFSP APPROVAL FOR A DISCOVERY FLIGHT!
We will keep updating this article as policies change. A lot of club members have experience with the AFSP procedures. Please reach out to us or post on the forum if you have any questions!