You are on the right track. First of all, here's a few pros/cons to help you make your decision:
-PROs: can run lights, charge battery, run stereo, AT ALL TIMES without running the main motor. This could be helpful for you if you are going to be parked alot (which you likely will be) or want to set up a dance party in the deep playa or whatever. Also a secondary source of power, should you have trouble with your charging circuit on the mower.
-CONs: $$$expense. There's really no other cons, assuming you are talking about a honda-style generator invertor. Don't even bother with the other style gennys that have to run full steam 3600 RPM at all times to create 120V @ 60 Hz. They suck, you do not want one on your MV.
-PROs: with a few hundred bucks and some know-how, you can solve your power issues with what you already have. MUTANT COOL!!!!! Who says you should always take the easy way out?
-CONs: depending on the size of your power needs, battery bank, etc, you might need to leave your MV engine running to produce power. Waste of Fuel, Overheating, etc? Wild Card.... You never know how an engine like that will react to the playa...
Now - with 23hp, I'd say, you have PLENTY of power available to drive an alternator. And, with a PTO lever you can use to engage/disengage the alternator, you can disengage to get the motor running (cars do this automatically) and you can also use gauges for voltage and amperage draw to determine when you need it connected and when you don't. PERFECT.
A little googling, says that alternators are a little better than 50% efficient. So, lets say we buy a GM 100 amp alternator. Output from Voltage regulator to charge a battery is around 14.5 volts. 14.5v x 100A = 1450 Watts of power.
At efficiency of 50% (these are mechanical losses, friction, etc) 1450W / 50% = 2900W - this is the amount of power required to drive the alternator.
Now, 1 horsepower is equal to 750 Watts. So here we go: 2900W x 1HP/750W = 3.86 HP or roughly 4 HP.
I guarantee, that spinning the mower blades in thick wet grass took at least half of the motor's horsepower, so no doubt you have plenty of power to do this. Just think, a 22 inch mower has 5-6HP these days, so double that or more and you get the idea.
Some other basics: A single 12V Battery of the Marine/RV - Starting/Deep-Cycle variety has a capacity of about 85 amp-hours (Ah). This means, it can put out 85 amps of power in one hour before it's dead (it will always be less) or it can produce much more power than that over time at a lower load - say like, 10A-20A.....
So what kind of power will you draw? Depends. I don't know what kind of MV you are planning to build, but I have built one electric and have worked on many others. Last year, I did a bunch of work on my friends Death Hearse. Totally rewired the MV part.
Main power draws are: Headlights, Stereo, Taillights/Running Lights, AC Inverter (to run flame effects), and interior LED lamps. Yes, of course you need a stereo!!!!
If I was you, I'd get two of these batteries wired in parallel to ensure you have plenty of juice. This will let you run your lights and stereo when you are parked and NOT running the engine. I have had two of these batteries from Costco that have lasted since 2006 and they are still running strong. About 60/70 bucks each.
Now, name redacted has a point. In spite of adding a second battery to the death hearse to run the peripherals, we still had problems with the motor battery running dead. Since the GIANT cadillac motor is running at idle speed all over BRC, that particular alternator isn't spinning fast enough in BRC to make a charge!! We are sick of this problem. You might have it too.
So what to do?
Well, you will need to figure out what is the sweet spot for RPM on your MV motor, and then find out what is an appropriate RPM for your alternator for good output.
First, the motor RPM - drive it around and figure out what feels right, preferably with the sort of load you'll have on playa. Now, you need to measure the RPM of the PTO drive pulley on the mower. HOW?? With one of these cheap optical tachometers: http://www.amazon.com/AGPtek%C2%AE-Professional-Digital-Tachometer-Contact/dp/B004Q8L894/ref=sr_1_4?ie=UTF8&qid=1395522976&sr=8-4&keywords=optical+tachometer
Simply put a piece of relective tape (included) on the pulley, and Voila!!
Second, once you have chosen the alternator you will use, look up the performance curve for the alternator - this is a simple graph, showing you what shaft RPM of alternator will get you X amps of charging power. Example:
OK, how to use this info? Let's say we have the alternator with the purple curve, it's closest to our 100A (but keep in mind, you need the curve for YOUR alternator!!) so the curve starts to flatten out at around 4000 RPM, is flatter at 5000, and ends at 6000. Let's use 5000 RPM for our alternator.
Let's say, with the tachometer we measured the cruising RPM of the mower engine at 2500 RPM - at the PTO pulley we will use to drive the alternator.
We need to covert this 2500 RPM to about 5000 RPM on the alternator - how will we do this? Gear Ratios. Say we measure the diameter of the PTO pulley at 6 inches. If we were to use the same size pulley on the alternator, we'd have the same speed as the engine - but we need twice the RPM. We can get that, by reducing the size of the pulley on the alternator. The ratio that we need, is 2 to 1 (2:1) gear ratio. So if the PTO pulley is 6 inches, we need a 3 inch pulley on our alternator.
What alternator to use? Well, I know that I've read posts in the MV forum form Cap'n Goddammit where he swears by a certain alternator that is powerful and widely available at pick/pull junkyards. He says that the dust regularly takes them out, so he always has a few spares for the week. Only trouble there, is you need to make sure you know what model it is to get the right performance curve, or someone's say so as to what RPM you should run.
The type that you want, without a doubt, is what is called a "one-wire" alternator - these have the voltage regulator on board so that you are always putting out a charge voltage around 14.5 volts. All you do is connect the wire to the positive on the battery bank, and ground it to the battery and you're set.
Hope this helps.