on a saved transaction search of Sales Orders - is there a field to indicate if the SO has >= 1 Item Fulfillments?

I doubt there is a field for it. You could try counting on the unique ids of the

applying transaction

of the correct type, but im not sure how easy that would be.

I would start with a search of SO, Mainline = F. Then in a Formula field add the Internal ID as suggested by Sandii. Group by SO, Count on Formula. That will give you the numbers. To filter it to >= 0 you would use Criteria Summary.