First off, I have no experience with this engine or any documentation for it either. I do have an extensive background in automotive and heavy truck repair but currently only work on carburetor equipped Hondas. Others here will probably have better information for you. With that said;
Yes, I believe there should be a "base idle" setting adjustment procedure that your dealer probably should have already performed in addressing this issue. Your throttle body does have a "set screw" listed in the parts breakdown and that is what I would think is used to perform base idle setting. And, I agree with you that 650 rpm at idle seems a tad low but, again, I have no documentation to back that statement up. These would be talking points for you and your shop or mechanic.
It's always a good idea to approach an issue like this from the simplest solution and escalate up. So verifying the idle speed is a good idea just as you intuitively concluded. Also, I see from a parts breakdown I looked up on boats.net, there is a filter for the EAC (electronic air control). It might just need cleaning. It is another good point of discussion with your mechanic.
Other things that come to mind that would give you a similar problem and might not log a code are, in no particular order:
Faulty EAC. Sometimes hard to verify without just trying a known good one.
Inlet air temperature sensor or engine coolant temp sensor out of range keeping the computer in the cold start enrichment mode too long and causing fuel "flooding".
Throttle position sensor faulty. Can cause a problem but still be "in range" and fool the computer.
"Lazy" switching oxygen sensor. Not too likely but should be looked at closely.
Map sensor. These are notorious for causing problems and not flagging a code in the computer. However, they usually cause power complaints not idle problems.
Dirty throttle body bore or throttle plate causing air restriction entering the engine at idle. Cleaning with carb spray can sometimes help although it could also void a warranty as special coatings used on these surfaces (usually teflon) can be affected by too strong a chemical. Use caution here.
Faulty knock sensor. As engine transitions from off idle to idle, harmonics could be causing the sensor to retard timing. Pretty unlikely but you never know.
This appears to be a COP engine. Meaning "coil over plug". These are common in the automotive world today but can exhibit problems with the ignition system that can be hard to diagnose. I hope your problem is a simple fuel ratio problem and not a complicated electronic issue.
Good luck.