Will deleting a project in Roadmap also delete it in Basecamp?

No, deleting a project in Roadmap will not delete it in Basecamp.

If in Roadmap... Then in Basecamp...
Delete project synced with Basecamp Nothing. Deleting project in Roadmap will NOT delete it in Basecamp.
Disconnect project (i.e. remove from sync list) Project status will remain unchanged. Updates in either app will no longer be reflected in the other.
Close project Project status will change to archived
If in Basecamp... Then in Roadmap...
Delete project synced with Roadmap Project status will change to closed
Archive project Project status will change to closed

Related:
Deleting projects
Bulk close (archive) projects

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