Very short answer: YES!!!!!!!!!!
Much longer answer: IN fact 18Ga for a 4 watt (1/3 amp) device is actually over kill.. Serious overkill.. It could easily run 10 or 20 of them.
That said: The above is looking at it from the LOAD side.
Now looking at it from the SUPPLY side.. 18 ga is a small wire, and if you try to push too much current it can quickly overheat..
Thought I had a chart handy (it's burried in a book that is in a different room) showing how much current 18ga can safely carry.. But I'd not go much over 10 amps on that wire.
A "rule" in electrical work is NEVER connect a smaller wire to a larger wire less you insert a fuse to protect it.. For this circuit I'd go with 5 amps on an inline fuse.. This is for fire protection.
That said. 18 ga will last much longer than the fuse in the event of a dead short even if the fuse is 20 amps or more.