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In most cases true on the starter battery being charged however the newer chargers play a very important roll in battery health and longevity with the maintainer phase as well as de-sulphanating of the battery plates (this is what causes most batteries to prematurely go bad)
That charger looks solid. It is 3lbs lighter with and extra bank over the one I have.
You would be fine most times I am sure. Personally I like all batteries being maintained when I'm not using the boat, weather it's a week or a month at a time. Non Lithium batteries can drain up to 3% charge per day just sitting, more so if they are old or lower quality even. If it's sitting for a month, it could be dead.