SQL Server - how transactions and transaction log work (simplified)
No your theory is wrong.

Dirty pages can be written to disc even if the transaction is not yet committed. However it is ensured that they cannot be written before the last transaction log entry that modified the page has been written to disc.

The transaction log records do contain sufficient information both for redo and undo (except for in tempdb where only undo is necessary). If you decide to rollback the transaction then nothing is deleted from the log. Instead compensation log records are written to the log indicating this.