I am planning migration from old SQL server 2000 db to 2014 (through 2008 extra step). I Wonder if stored procedures will work with no tweaks or arrangements are required
You should check breaking changes.
you can use upgrade advisor or
dbatools - Test-DbaMigrationConstraint
This function only validate SQL Server 2008 versions or higher.
For the most part...yes. However, there is no way for anyone to be certain. I would suggest you run the Upgrade Advisor to scan your database for potential issues. https://msdn.microsoft.com/en-us/library/ms144256(v=sql.120).aspx
The tool will tell if you are doing anything that is no longer supported in later versions of SQL Server. This will catch about 90% of the issues that you may encounter.
Besides running this tool against your database, you want to test, test, and test again. This will be the only way to ensure that your applications will work post upgrade.
This is something that needs to be tested since many commands have been deprecated between 2000 and 2014. Assuming you are moving the database to another server I would test this first.
Restore the database to 2008 and then to 2014 and then attempt to run each procedure. You may even be able to use the distributed replay controller feature to automate this. On the 2014 server try to start a profiler trace with the DRC template against your 2000 server. Then do a test migration and replay it while running an extended events trace for deprecated commands. Some procedures may even fail to run outright.