Is it possible to use a stored procedure to read the file inside the blob column, loop on each line and insert the data in a table?
Definitely.
However, I would consider rethinking this plan.
A SQL Server database generally isn't a great place to be storing BLOBs, particularly given that you're just going to turn around and process them into row data later. It's a lot of extra disk activity and (presumably more expensive) storage that you just don't need to use. Also, the kind of processing being proposed will almost certainly perform worse than the many direct-processing alternatives. Generally speaking, the less processing you need to do (and the simpler the process itself), the better performance you'll get out of the system. And it will probably be more reliable as well.
Why not turn the files into row data immediately? Are you concerned about blocking or latency of the client application? If that's the only concern, consider setting up an asynchronous queuing system, possibly by using Service Broker. You can use BULK INSERT to turn the CSV files into row data directly from the file system without first loading the files as BLOBs. If this is going to blast the CPU during load when you need to run other things on the same server, consider using Resource Governor if you're on Enterprise Edition.
If you have to process the files in batch at night due to other constraints, it may be better to simply direct the raw files into a named (YYYYMMDD) folder on a network share during the day, and then once/day use an SSIS package with a Foreach File Enumerator container to process the files. I suppose this could also work in a job-based scenario where you just fire it up every 15 minutes or so to process and remove files that landed in the folder in the last period. SSIS may also be a good solution if you need some kind of transformation process to happen between the raw files and the row data.
There are lots of different possibilities here depending on your exact requirements, but I think I've given enough of the more common elements that you can piece together a solution that will work best for your situation.
This seems very similar to:
From that Microsoft Support article:
Symptoms
Assume that you use the RESTORE HEADERONLY or RESTORE FILELISTONLY command to restore a database from Windows Azure Blob storage service in Microsoft SQL Server 2014 or SQL Server 2012. After the command is completed, you cannot remove the backup file.
Cause
The issue occurs because there is an infinite lease on the backup file. Some race conditions between internal threads cause the lease to be not released in some cases.
This is marked as first fixed in Cumulative Update 4 for SQL Server 2012 SP2. While the fix does not mention RESTORE VERIFYONLY explicitly, you should definitely check this out before reporting it as a bug.
The latest Service Pack for SQL Server 2012 at the time of writing is SP3, which will also include the fix mentioned above.
Finally, just to document something GregGalloway originally left in a comment on the question, you can remove active leases using a script in the following MSDN article:
Deleting Backup Blob Files with Active Leases
Best Answer
I have experimented with the tool and confirmed that deleting the stub files does not delete the Azure blob. I had to set up a PowerShell script to cleanup the file blobs.