Sql-server – Will Ola’s default IndexOptimizer job update the stats

You can see how many rows were sampled (among other things) by using the sys.dm_db_stats_properties DMF:

SELECT object_name(s.object_id), s.name, 
       sp.last_updated, sp.rows, sp.rows_sampled, 
       sp.steps, sp.unfiltered_rows, sp.modification_counter
FROM sys.stats s
CROSS APPLY sys.dm_db_stats_properties (s.object_id, s.stats_id) sp
WHERE s.object_id = object_id('TableName')
AND s.name = 'IndexName';

You can add some math to do the comparison for rows_sampled vs rows. Given that there will be data movement in the table after you update stats, I wouldn't expect this to be 100%, but you can assume that if a full scan was done, you'll see at least 80% of the current table size:

SELECT object_name(s.object_id), s.name, 
       sp.last_updated, sp.rows, sp.rows_sampled, 
       --
       sample_percent = (100*sp.rows_sampled/sp.rows),
       --
       sp.steps, sp.unfiltered_rows, sp.modification_counter
FROM sys.stats s
CROSS APPLY sys.dm_db_stats_properties (s.object_id, s.stats_id) sp
WHERE s.object_id = object_id('TableName')
AND s.name = 'IndexName';

Now, you just have to use some tool to run it against your thousands of databases. I suspect that if you're managing thousands of databases, you already have an established way to do this. As a PSA, I'll mention that sp_MSforeachdb sometimes misses databases, so consider avoiding that stored procedure.

The new calculation is only used if trace flag 2371 is enabled, except on SQL Server 2016 when the context database compatibility level is set to 130, where it is the default behaviour. See Microsoft KB 2754171:

Controlling Autostat (AUTO_UPDATE_STATISTICS) behavior in SQL Server

Statistics are not updated when data is modified. A statistics update is triggered when cost-based optimization finds that interesting statistics for the query are stale.

The optimizer does not enter cost-based optimization for very simple ("trivial") queries, where a single obvious plan is always optimal. No statistics updates occur in that scenario.

See the Microsoft White Paper Plan Caching and Recompilation in SQL Server 2012 by Greg Low.