I think it's a bit more complicated than running it through a filter, otherwise we wouldn't have to worry about ever running out of water. I just think your plan of going to a deserted island, while innovative for sure, is fundamentally flawed. Also, using a filter means that it'd get clogged after some time, what size filter do you plan on bringing?
I'm just doing some CoA analysis here, war gaming it if you will. I'm having a house built up in the mtns of CO that'll run purely on solar and wind power (never run out of energy!) and in close proximity to a water source. Just saying that that is a better option than stealing a boat, going to some unknown island with a limited food/water/fuel/ammo supply.
Advantages:
1. Self-contained power and plenty of firewood as a contingency
2. Reliable natural food/water supply
3. Can always run down to a local town for target practice, fuel, matches, ammo, etc.
4. We can keep our vehicles, and if we ever get froggy, make it to a NG Armory OR Ft. Carson and take vehicles, weapons/explosives and ammo. Imagine having an up-armored LMTV to roll around in for supply runs.....just saying! Plus, we can get a couple MK19's for Gino to slay zombies with!
5. Way more contingency options than an island.
Disadvantages:
1. Slightly higher risk of zombie interaction.
When you get tired of your island, feel free to make the trek to my mtn retreat where me and some of my best buds will be living the high life like Miller. Which brings up another point, beer. How do you plan on keeping a constant supply of beer? Coors plant AND Budweiser plant are in.............you guessed it! Colorado.
Feel free to analyze my plan and see which one works better. Once again, not trying to down your plan, just trying to develop a plan with a higher rate of survivability.