I think it does.  I have been a believer in Synthetic for many years.
I have been using it for many years, especially in air cooled engines
that can get extra hot.

If you are using multi grade I strongly suggest it.  Conventional oil
needs Viscosity Improvers (VI) to get the the oil to the desired
viscosity.  Synthetics can do it without using VI.  So what you might
say it that 5W30 Mobil 1 is similar to conventional straight weight 30
but it doesn't get as thick when it gets cold.  Then there is the added
advantage of being able to withstand heat.  From what I hear normal oil
begins to break down at about 350 degrees whereas synthetic can go to
700 or above.  There can be spots in an engine that get to 350.

So it costs a bit more.  Many say you get a little better mileage in a
vehicle (and I believe it).  I guess a generator should put out a little
bit more power so you might use a little less fuel.

I decided to do a little web searching on the subject.  Quite a few hits
such as:

http://tinyurl.com/pm9y2

Many seem to be using 15W50 but I don't believe in using any heavier
weight than necessary.

If you are one of the .001% of rver's who actually put enough hours on the
genset to change oil based on the hourmeter rather than the calendar date,
then feel free to use synthetic if you care to. All I'm trying to say is:
   -Most rver's put so few hours on their genset that - if they follow the
manufacturer's recommendation - they change the oil based on the date i.e.
change oil every 6 months or 150 hours whichever comes first.

   -With so little use, the oil doesn't 'wear out' - you change it so that
acids and other things from combustion byproducts don't start eating things
from the inside. Synthetic oil is no better than regular oil at neutralizing
these.

   -As long as you maintain them, the Onan generators under discussion
should easily exceed 3000 hours on regular oil before they need rings or
bearings. The average genset in an rv gets less than 50hrs/year of use
(sometimes FAR less). Do the math - you are unlikely to see any benefit from
synthetics while you, your children or their grandchildren have the rv.
Perhaps the great-grandchildren might notice that it still runs pretty
smooth <g>.

Now, if you go to Burning Man every year, and sit for a week in the Black
Rock Desert running the genset 24/7, then you might consider synthetic
oil...

Alan