Trello is an Atlassian product, and while I don't use Trello myself, my company uses many of their other products (Jira, Confluence Atlas, etc). I am fairly certain their permission settings work the same (or very similar) across products. From my experience with their other products, yes, you can allow users to view the board without creating an account. However, it would also be visible to the public. I don't believe there is a middle ground in which you can permission a group of users to view the board without logging in. More than likely, the board either needs to be visible to all (public) or the users will need login credentials for Atlassian to which you've given permission to view the board.
Per Trello's documentation, when a board is public they set the robots rule to no-index, no-follow. This means that, yes, anyone with the link can view your board, but the link to your board won't be indexed in search engines.
Public boards are visible to anyone on the internet, but not indexed by search engines such as Google. Anyone with the link can view a public board, but only board members can edit it.
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Brandon Scivolette
Technology Oversight Volunteer
Rebels Rescue, Inc
FL
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