I am the DCT at a program like this, so I can speak to this situation a bit. As others have said, I would strongly encourage you (and an advisor you trust at your current institution) to speak with the DCT to learn about the steps the program is taking to ensure that the courses are equivalent to an APA program and that the program is moving forward promptly toward APA accreditation. In our case, we have three cohorts of students already in the program and are beginning to work on our self-study. Because of this, we plan on applying for accreditation very early in the graduate careers of the students we admit. While we cannot guarantee that we will become accredited, and there is always more risk going to a non-accredited program, the students we accept this year should know the outcome of our APA application well before they have to apply for internship. If we were somehow unable to attain APA accreditation and a student asked me for a letter to apply elsewhere I would have no problem providing a very strong letter explaining the situation. Thus, it is my hope that the risk, while certainly present, is minimized for students coming in this year.
Every program is different, and is in a different place in their preparations for APA accreditation. Again, talk with the DCT, it will be well-received. I personally look forward to discussing this issue with students on our interview, and I view discussing it as an opportunity as I believe our university provides very strong training and that we are making great strides towards applying for APA accreditation. As I mentioned before, if you have any trusted mentors at your school, perhaps have them talk with the DCT as well? You want to make sure you are comfortable with the school regardless of if it is accredited or not, so take advantage of your mentors!
To respond to an earlier comment, I know that our program, as well as several other university-based PhD programs that are new and currently seeking accreditation, offer competitive funding and tuition waivers.
I hope that is helpful. I will try to check in on this thread if there are any questions I can answer, but also please feel free to message me if you have any questions.