Not only some, but in fact most GA propeller-driven aircraft have propellers that extend below the bottom of the fuselage. (The only exception that quickly comes to mind is the Cessna Skymaster; I'm sure there are plenty of others.)
Note that the aircraft will have some secondary method of gear extension, such as gravity drop, a manual crank, or a blow-down bottle. But there are still times where the gear cannot be extended and locked.
In this situation, you've got one emergency. Don't make it two emergencies by shutting down your engine. There's an aphorism - "If the gear fails, the insurance company just bought the airplane."1 Without gear, you're going to do some damage: scraped belly, probably tearing off some antennas. The aircraft will already require maintenance; the extra time and cost of an engine teardown is insignificant compared to the increased risk from a higher workload and a landing that the pilot may not have ever practiced before. (The approach with gear up and engine out will be different than that with gear down and engine at idle in a simulated engine failure.) Don't risk your life to save the insurance company money.
Additionally, just stopping the engine isn't sufficient to prevent a teardown. You must also rotate the prop so that it's horizontal, which requires slowing substantially as you pull the mixture to stop it from windmilling, and then using the starter to move the prop.2 You'd need to prevent any substantial contact between the propeller and runway, as Lycoming's Service Bulletin on propstrikes that require inspection and repair (Continental's is similar) includes the situation of
Any incident, whether or not the engine is operating, where repair of the propeller is necessary
After all of that, there are some best practices:
- Declare an emergency. ATC will help you, have equipment ready on the ground, and clear traffic around you - but they need to know about it first.
- Use your checklist. An airplane with retractable gear will have an entry for gear failure; follow it. In particular, you'll shut down the electrical system before landing, and probably brace open a door for exit.
- Land on a paved surface. Dirt or grass may seem softer, but they aren't as smooth. According to an AOPA flight-training newsletter, "Statistics suggest that putting the airplane on the asphalt is likely to cause less damage to you and your airplane than putting it on the grass."
(1) I've also heard "The insurance company buys the aircraft when you take off; when you land safely, you buy it back."
(2) Or you could do it in the flare - a suggestion so dangerous I include it only for completeness.