Yes, their watches are typically authentic, however it will cause you nothing but grief to get an Omega without a serial number. Especially if you want to have it properly serviced by an authorized Omega service center or retailer. They may refuse to service a watch with no serial numbers, perhaps even confiscate it, and at the very least it's embarassing to walk in and ask them to service a watch that's quite clearly of dubious origin. It's also not worth it since there are plenty of sites that offer wholesale price Omega's with the serial numbers still intact. BuyJewelsDirect.com and AaronsWatches.com are two that I've bought from in the past, BuyJewelsDirect an Omega Speedmaster Day/Date and AaronsWatches a TAG Heuer 2000 Excl.Chronog.. A good price comparison site is Pricescan.com. Then, as you're checking out each vendors page, e-mail them and ask whether or not they remove their Omega Serial Numbers, and how much would a model cost with the Serial Numbers intact. If they do make a practice of removing them, they will usually offer you an intact model for a hundred or two more.
Here's another good way to look at not buying from an authorized retailer yet having the serial numbers intact: All the money you save on the retail price, if there's a problem with your watch just take it to an authorized service center and have it fully serviced. The service center will then gaurantee it for One additional year, which is great because they are factory authorized. Even better, you're still saving tons of money off of the retail price. Even if you get the most expensive type serviced, e.g. a Seamaster Automatic Chronograph (which can cost up to $300 for a full servicing) if you bought it for only $1400 with SN's intact, you've only paid $1700 in the end. You're still saving $1000 off of the retail price. I mean, I've done all this figuring and research because I love Omega's (I own 4), but I just plain don't make enough money to buy them from authorized merchants. This way, I save hundreds, and I also get to wear the best timepieces there are!!