Any additional support will help but the truss won't hold the load as originally designed. That truss is designed to spread the load and seeing that the truss you have are made with 2X3's you have compromised a lot of the strength by removing those members. I see you have sistered 2X4's to the bottom cord which will help with the storage load. Don't get me wrong. I don't believe the roof will suffer a major collapse, but the roof decking supported by the 2X3's where the cross bracing was removed may sag over time. Usually truss as you pictured that are open are attic truss, and are made with a combination of 2x4"s and 2x6's or 2x8's or larger depending on the load and span specs.
I have a small shed that has a 15 foot span and has open truss (no webbing) but the top rafters are 2X6's with a 2X4 bottom cord.
