You will be scrubbing that moly out of your bore for a long time even with any special cleaners. A simple liquid/gel dishwasher detergent works just about as good as any of the magic cleaners that the gun shops sell. And...LOTS of elbow grease with a bronze brush!
BUT...once you've fired a few rounds, the heat will turn some of that moly deposit into Moly Trisulfide which bonds itself to the steel in your barrel and there isn't any really good way to get that out of your barrel except an abrasive (like JBs Bore Paste or valve lapping compound)...this is hard on the barrel though. You might wind up ruining a perfectly good barrel trying to get the coating out of it.
Much like copper fouling fills in larger voids in a barrel, moly disulfide will build up in your barrel too...but since the particles are so much smaller, they'll get impacted into even tinier voids in the barrel steel making it that much harder to remove later on.
The biggest problem with moly coatings are the sulfur and sulfur oxides that they contain...they'll mix with any moisture in the air to make sulfuric acid. This is what will cause corrosion.
A good link I've had bookmarked for a while on how/what/why moly does what it does:
Yeah, that company is pedlding a moly lube to use instead of moly coated bullets...but that whitepaper still does a good job of explaining the action/reaction that any moly does when used in a rifle barrel.