Looks like there is enough depth there to prevent them from falling over, even in perlite. Probably depends on how tall you plan to grow them. If you scrog or sog then it shouldn't be an issue. Although the roots will take over those trays within no time I rekon. By the way I'm a big fan of perlite. Its a great medium. I'm nearing the end of my first hydro test grow using it and I can't say enough good things about it. I have been logging my progress and will post a thread when/if it finishes successfully.
I know you are a very experienced hydroponics grower but have you used perlite before?