In my experience, whether you have First/CW tags on or not won't make a jot of difference to how your baggage is handled, any 'priority' handling is down to the barcode.

There are some who say that First tags are purely there for the 'DYKWIA' factor. If you disagree, and are concerned about OSL not having suitable tags, why not print some spares at home, just in case? Here's the latest iteration: