Dike district land, from my experience in Skagit County, is typically a "no", unless it is part of an established WDFW hunting area.
The WDFW website mapping does not show Game Reserves, at least last time I checked. So be aware of those. Their mapping just has them the same color as other DFW lands that are open to hunting. Very confusing for newcomers or internet research.
The land next to Spud House has very limited opportunity, if any. It's mostly cottonwood forest, and the small plot of ag land is leased to a farmer and not really huntable. At least I wouldn't recommend it. There are Private Lands/Quality Hunt areas nearby if you want to hunt fields.