The short answer is “YES.”
In the old days prior to the Internet, LES statements were delivered via the fiance office to the orderly room. From there they were checked by unit leadership to ensure people were receiving the proper amount of pay and entitlements, and to verify leave balances. Nowadays I believe this information is available in a Commander’s roll up report.
There is nothing against the unit requiring Soldiers to provide a copy of their LES. Your LES is an official military document. Think of it as an employer reviewing pay stubs. This allows the commander to ensure leave is accurate, any special pay is accurate, etc.
However, the command CANNOT force you to provide your personal banking information (bank statements, personal loans, etc) or any additional information about any personal allotments on your LES besides the amount. You can provide your personal finance information voluntarily if asked by your command, but you cannot be forced.