If your block is associated with a specific topic, then the answer is yes.
What you can do is add the &topic variable to the link you use for the static page.
For example:
yourdomain.com/staticpages/index.php?page=20030919&topic=88GClash
Displays the static page 20030919 and any blocks related to topic 88GClash
For example of how this works in practice look
here[*1]