So, AADSAS said your scores were sent out with your application? If this is the case, then you're probably fine.
Something you might consider doing, if AADSAS continues to be unhelpful or slow: contact a school you know has received your application (perhaps they sent you an email or made an update on your AADSAS for application received), call their admissions department and ask to verify that they received your DAT scores with your application. If they say yes, then clearly you're fine.
Based on your thread title I am left wondering if you believe you will be seeing your actual scores posted? All you will ever see in this section of your application is the date, no actual scores.