No. Your Sideline business contacts are not displayed nor synced on the Web version of Sideline since Sideline Web Messaging does not support the Sideline Pro features at this time.
Simply put, any changes you make in Sideline Pro to your address book/contacts, it will not sync with the Web.
More information on this incompatibility and how it impacts the core features (Broadcast, Shortcuts, and Reminders) can be seen in the article 'Is Sideline Pro compatible with Sideline Web?'
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