How to do Incremental statistics on auto_created stats(_WA_) in SQL server
You have the default settings.

is_auto_update_stats_on= True; 
is_auto_update_stats_async_on= False;


So when you run a query that needs updated stats, the stats will update before your query runs.  You could update stats more agressively, or allow the query to run with the old stats while the stats are updated by turning on 'is_auto_update_stats_async_on'.

And yes, modifying an auto-created statistic to be incremental appears to work fine.  eg in AdventureWorksDW after partitioning FactInternetSales:

ALTER DATABASE current SET AUTO_CREATE_STATISTICS ON (INCREMENTAL = ON)
GO
UPDATE STATISTICS [dbo].[FactInternetSales]([_WA_Sys_00000004_4E88ABD4]) WITH INCREMENTAL = ON
GO
UPDATE STATISTICS [dbo].[FactInternetSales]([_WA_Sys_00000004_4E88ABD4]) WITH RESAMPLE ON PARTITIONS(2)
GO