It's not really about the overall capacity (120AH) which could be 120A current drawn over 1 hour or (at the other extreme) 1A current drawn over 120 hours, but the cranking (i.e. starting) capacity, which is the ability of the battery to support the heavy duty starter whilst you start (how much current you can pull out over say 10s is largely determined by the cell construction).
If this is your outboard: http://www.tohatsu.co.jp/en/boat/pro...0A2_110207.pdf
then the manual says:
Minimum recommended battery :
12V, 70AH (800 Marine Cranking Amps (MCA) or 650 Cold Cranking Amps (CCA))
I'm not sure which actual battery you are looking at, but you just look for a specification for MCA or CCA which you need to match against your outboard manual. I tend to go a little bigger on both CCA and AH requirements just for safety, but you don't have to!
Forgot to add - the alternator output just indicates how quickly you can charge the battery (but the alternator will not charge at 27.5A unless you have reasonable revs) - so on the plane at 3500 rpm I'm guessing that you would get 20A and if you sustained that for 1 hour then 20AH would go into your 120AH battery (so it would take 6 hours of continuous running to charge fully). Hope that helps !