Since REM cycles get longer and are more frequent the longer you've been sleep, yes. Also, maybe you didn't have time to remember your dreams because you had to wake up early and get ready for school right away.

Last night, after only a couple hours of sleep I woke up and remembered my dream pretty well, and wrote it down. It seemed about as involved and otherwise similar to any normal dream I'd have that I'd usually remember after 6-8 hours.