Yes....by thinking outside the box and running with a solution whereby "you monitor under intense supervision" from your production support team. SOX doesn't say "Developers can't have ANY access to Production". Sox says "You should put firm documented policies and procedures in place to ensure adherence to good practice (both IT + Operational) - re seperation of duties in normal operations. And to ensure reasonable, documented and supervised policies and procedures re access, etc exist to handle unusual out-of-course operations". Once the access to production is logged and monitored, then compliance with SOX is inbuilt.
Alternatively you backup your database to another server, and periodically re-apply the production transaction logs on the backup server (step by step debug style), when you encounter a deadlock problem. It might not equate to active monitoring, but at least you can come close.
One other way to your objective is to create (buy) and deploy a health-check appliction, which monitors KPI's of the database...ie throughput, average i/o, problem queries, etc....and let it do the monitoring for you.