With the arrangement that I believe you have, it comes out to yes, about 3.3W. So to run it 10 hours would use 33WH of power dissipated by the LED module itself.
The losses, assuming the datasheet for the converter is accurate, are about 7% for nominal 12V, or 93% efficient. Call it 90% efficient to make math easy, and give a little wiggle room.
So for every watt in, 100mW will be wasted as heat in the converter. To get your 3.3W to the LED, you'll be pulling just shy of 3.7W from the batteries, losing ~0.4W as heat.
This works out to 37WH, which as I mentioned earlier, is really stretching it health-wise for 108WH of battery, at just over 33% of capacity. Depending on design, the batteries may or may not tolerate this well. You mentioned they were for cranking a lawnmower; batteries designed to crank generally aren't set up for deeper cycling than a few percent of capacity. On this small of a scale, tho, I couldn't say for sure. If not, a few sunless days and the grim reaper will visit them early. 
As for a charge controller disconnecting the LED from the battery when the voltage drops to a certain point, yes, some do. The caveat here is that you'll probably spend more on the charge controller that does this than all of the other components combined (based on what I've seen so far).
http://www.windsun.com/ChargeControls/ChargeCont.htm has a down-n-dirty explaination of what they are, when they're needed, and what they are and aren't designed to do.
A undervolt cutoff could be done much cheaper with the DIY approach: A comparator chip, a few resistors, a zener, and a MOSFET as the master disconnect. I'm assuming you're already going to be using a light sensor of some sort to shut it down during the day, right? It wouldn't be hard to integrate the cutoff circuitry into the existing schematic. Consider a timer circuit as well, shortening even to 5 hours each night will improve your margins a good deal.
And like I said, for the charge control itself, all you need to do is dump the surplus once the batteries are full. A single zener of appropriate power handling will work beautifully for this since you're talking such small quantities of power.
As for being new, experimenting is how you get your wings (sorry guys, couldn't resist). And yes, concepts and real world don't line up perfectly, leading to deeper thought than what is on the surface. But tweaking concepts is what this place is all about. Don't be afraid to try things, just use extra caution when either of the following two circumstances are present:
- - Expensive parts. It really sucks when you let the magic smoke out of something you just payed really good money for. Cheap components? Eh, who cares. Dime a dozen...
- - When you or someone else around you could be in danger as a result of your experiment. A couple trips to the ER have taught me a thing or two...
Generally the latter doesn't apply to things like solar porch lights...
Other than that? Don't be afraid to ask. There's good people here. Many very knowledgeable. As long as you've done a little homework (ie you're not trying to power your house from a 9V battery and a garden solar light), they're usually more than happy to help.
Steve
