If you had Iron hooked elsewhere and already available to your hypothetical tile-shifted Alexandria, then (I think) you would be able to build a town-improvement which "Requires Iron in the city radius" even without a direct connection from the Iron-island to your trade-net, but otherwise no.
As Bartleby says, to actually use that Iron (whether to build units, or to trade it away), then yeah, you'd need to plant a town on the Iron-island, and give it a Harbor.
This can be seen if you play the Sengoku conquest: there is a 1-tile Hill-island just south of the Miyoshi/ Matsunaga spawning area, which has Saltpeter. The only way to obtain that Salt is to Settle it.