Yes! To create a share link that doesn't allow for downloads, follow these steps:
Locate the board you want to share
Click on the "..." button on the board preview
You will see a dropdown menu with options. Select Share
From the Share screen, you will see a few options: View assets, Download assets, Upload to the board, Upload without being logged on, Show all versions, Allow public comments, and passcode protection.
Choose View assets only if you don't want to allow the receiver to download assets from the board