It's a shame to hear of this kind of thing, again.  Too often someone half-asses something with a generator and ends up dead for the 'bargain' they got instead of a legit setup.
I agree regarding the built-in ones being sensitive to voltage.  But this just means you need to add more house battery capacity.  I discovered the low voltage alarm at 3am one night while out on the hook (after a fine dinner and many margaritas).  Try reading the tiny print on the instruction pamphlet when half-in-the-bag.  Then try unplugging the bastards without ruining them.
I also now have a battery powered CO alarm onboard.  It's the kind with a numerical read-out showing the CO PPM.  Very helpful to know if it's just something trivial or a serious issue.  I do, however, still have the built-in ones installed and operating.  
Bearing in mind, of course, that CO exposure is cumulative.  Low levels over time as just as bad as higher levels for a shorter time.  And you really do need to offset your exposure for a fair bit of time away from it before you're truly safe again.
Anyway, this always reminds me of the 
despair.com poster:
