Yes and no, unfortunately, if I'm grasping settlements correctly...someone else please confirm this if you know for sure.
It looks like assigned resource items ARE shared among linked settlements, such as farmed food, purified water, and items collected at scavenging stations by a settler...but the armour, weapons, apparel and junk you collect and save at a workstation are NOT shared among linked settlements, which is a total bummer. That blows the possible advantage to survival mode, but keeps the odds more realistic (and fun). #FTR
As mentioned online last night, I just happened to be scrolling through my Pip-Boy and noticed that one of my settlements had grown from 2 to 12 without me noticing; they had 0 water, 2 beds, 3 food and no fewer than 4 Brahmin wandering around. I ended up going to Sanctuary, clicked Take All at the workstation, then fast-travelled to the new settlement so I could set them up without having to go back and forth a million times for a missing screw. When I got back, Sanctuary's inventory was empty save the water, food and scavenged materials that had accumulated in the meantime. I don't know if you have to have a provisioner assigned in both directions (so far mine are only Sanctuary-out), or if you have to close the supply line loop for them to be all interconnected.
For the record, I'm not an expert on settlements (yet), up till the Starlight population boom happened, I'd concentrated almost all my settlers in Sanctuary. I'd welcome more insights from you guys.