Or you batts could just be really low on charge and you need to rev the engine up more to "get her chargin"
Also, there are 2 ways to charge the batteries. Plug into shore power and let the electric company and your inverter/charger do it or turn on the engine and let the alternator do it. The two sources of charge are not normally on at the same time.
So to answer your questions, if the batteries are charged when you return to the boat for a new weekend/daysail then the inverter/charger is OK, and no the inverter/charger working does not mean the alternator works and viva-verca.
To trouble shoot this you need to turn on some high draw 12 volt systems like the reefer and freezer and start the engine. After reving up the engine for a few seconds to make sure the alternator should be running, measure the voltage AT the alternator output post (from the port engine access panel so you don't get 'wrapped up in your work"), then move to the battery isolator (blue box with cooling fins in the engine compartment, Just follow the alternator output cable), the center terminal should be at alternator voltage, the start and house terminals should be at alternator voltage minus about a volt or so, if that checks low the diodes are bad and the need replaced ($5.00 from digikey.com), the next stop is the positive battery terminals or any fuses in between, the voltage there should be only slightly lower than the battery isolation terminals. note that the start and house diodes on the battery isolation box are not the same voltage drop so you have to keep things straight)
To check the inverter/charger is real easy, just turn off the inverter/charger for a while and run the reefer and freezer. with shore power plugged in turn the inverter charger on and watch the voltmeter on the panel. It should show a distinct voltage rise withing 30 seconds or so. It will not show a voltage increase like turning on a light as it has to sit there and sense the voltage for a few moments so it can figure out what to do.
good luck
