It will 100% work. I use a California Air and Makita compressor for most of my at-home airbrushing.
A few tips to help you make it successful:
1. You absolutely need a moisture trap & particulates filter. Ideally, it's not attached RIGHT on the output of the compressor. Why: the air is hottest near the compressor, and as it cools, moisture condenses. So a moisture trap further away is much more effective.
2. Set the pressure on the craftsman to 60PSI or so.
3. Your compressor probably has 1 or 2 1/4" female industrial style quick connects. The simplest way to hook up an airbrush hose is to put a 1/4" male quick connect that has a threaded 1/4" NPT on the other end. You can just screw your airbrush hose to it that way.
That's not a good way to do it, unless it's just a hose to clean out your airbrush. Because where do you stick your moisture filter, in that scenario?
A better way is to hook up your regular hose on the compressor end, and hook up the other end of the hose to a hobby regulator + moisture trap, which kills 2 birds with one gizmo. Or, if you have a spray gun setup already, hook your hose up to the oil & water filters, and then hook a hobby regulator up that.
4. Set the hobby regulator at 20 or so psi.
5. Remember that when you use Teflon/PTFE/thread-seal tape, wind it CLOCKWISE. If you wind it counterclockwise, it will bunch up and shred as you tighten the thread and just make a mess (and leak).
Annnnnnd... that's it
By the way, reducer = regulator. It's just a screw going through the pipe that restricts airflow (like a water faucet). Most regulators will also have a pressure guage, so that you know what your setting is. But this isn't always true -- in the non-hobby world, many (most?) regulator/filter setups separate them, and even some hobby regulators like MAC valves don't have gauges.
Important attribute for a regulator is PSI drop. That is, when air starts flowing through it, some regulators have a bigger drop in the output pressure than others. It's not a huge deal, but 5+ PSI is common in industrial applications, and that's like, half the pressure I might use for a fine-line airbrush.
Generally, you probably want a hobby-style regulator/moisture trap rather than an industrial one. The reason is because they are a LOT lighter making it possible to easily suspend it with a ring, instead of having to have it mounted to a board; and also, they typicially have a narrower range, meaning it will be easier to set low PSI more accurately, or at least, more reproducibly.