I'd pass. As long as you use top tier gas, it really shouldn't be
that dirty. And if it were, you can go to the auto parts and buy
a bottle of Techron. That will clear it up.
But all the top tier gasoline's have cleaner in them already.
IE: both Chevron and Texaco use Techron. The other top brands
use their own proprietary cleaners.
I've had to clean very very severe carbon out of a Camry one time.
It was so bad, the engine wouldn't run once it warmed up due to
the carbon expanding and keeping the valves from fully closing.
And then no run..

I found that Techron is one of the better cleaners,
and it really does work.
I'm running an 05 right now with 60k miles, and I've never had any
carbon issues yet. Still runs the same as when I bought it.
But I do stick to top tier gas, and I prefer Chevron and Texaco due
to them using Techron. But I burn a lot of Shell too.. They use their
own "oxygen" cleaner. How it compares to Techron, I don't know..
Anyway, if you start seeing possible carbon issues, just dump a
bottle of Techron in the tank. That should clean it up.
All gas sold must have a minimum amount of cleaner, but the top
tier brands seem to have more of it. And the higher octane grades
usually have a bit more than the regular. So every once in a while
I'll dump some premium in the tank, even though mine runs ok on
regular without knocking. But part of that is due to the knock sensor..
It actually runs better and has more power with higher grades once
the car puter adapts to the higher octane.
45k miles is a tad early to be losing an alternator.. I'd think with
that low mileage, it would be covered under warranty..
Maybe it is, and the carbon cleaning is so they can actually make
some $$$ off you.. :/