From an operational viewpoint, you cannot reasonably expect this to work very well. One of the issues regarding any database is the ability to perform a full backup, which requires someone (usually the BackupOperator intrinsic account or someone designated to have the same privileges) to have the ability to trigger and execute the backup procedure, whatever it is. Unless, of course, you will do your own backups during non-operational hours. Don't know for sure about SQL Server, but on ORACLE that means the ability to tell the DB engine to enter "backup" mode while the backup is running and then leave that mode when done. And for ORACLE, that has specific implications about transaction handling. I'm only guessing for SQL Server, but it wouldn't surprise me to find they had something analogous to ORACLE's "backup mode" operations.
Then, if your site actually HAS a security team, I can tell you their answer... NO. Without access to the files, they will be unable to run a security scan checking for injected code - and SQL injection is a well-known security breach pathway. The IT security team will, probably by directive from the higher-ups in the company, have FULL ACCESS to everything on site to check for intrusions and for compliance with security standards.
From a whole-file viewpoint, you CANNOT prevent the SysAdmin staff from accessing the files. From a file-internal-structure viewpoint, some level of access might be blockable - until the SA exercises the right of the SA to take over ownership of a given file. At which point, a lot of forbidden actions suddenly become trivial. OR until the SA decides to do a Run As to launch some script that, because it has the right credentials, will be able to do whatever it was that you didn't want done.
Finally, if you are in a small company, many folks wear multiple hats. For smaller installations, the SA might also be the chief DBA. For a larger company, there still will be many hats to wear (just more heads on which to distribute them), but that actually would work AGAINST you since upper management will more likely believe in distribution of duties and won't LET you take full responsibility over operational issues if the database in question is important to the company's operation.
This is a case where technically, you might be able to do what you want, but politically it is extremely unlikely. And I hate to break this to you, but us tech nerds lose EVERY TIME to the political wonks. It's just the way of the world.