Assuming that you have permission from the system administrator or other database owner, you can certainly access the data inside the database. Depending on a lot of factors related to the ASP page and database design, the amount of work needed to do this might be small or large.
Conversion to MySQL depends on your ability to access the data at all. There are a lot of design choices in terms of getting data from your old site to a new one, and I'd need a lot more background to help someone with your experience to get the data moved.
The odds are very high that the task can be done. I don't know enough about the problem to even guess how much work that it will be.
-PatP