You most definitely can. Application is KEY though. If you're Jonny from Jonny Cycles and can rip a skid over 200 feet then I wouldn't recommend it. But for every day use, without abuse, it's ok. I have built many many conversions over the years spinning on a fixed cog without concern. Mind, I clean/degrease/alcohol/acetone the threads of both* very well, use Red Loc-Tite and either Rotafix or use a very long handle(d) chainwhip for torque.** If folks tell you it can't be done safely they are dead wrong. I have been working on bikes for over 15 years and have too much experience with this particular area to give you false advice. I have had grocery bikes, commuters, fixed MTN bikes, fixed trainers, etc. all with spun on fixed cogs and never had a problem. The first one that ever broke loose was one that my 200 pound skidding brother cracked free after over 2 years of hard use/abuse. BTW, when we race up at the track, you can take a gander and see how many of the P/1/2's have lockrings on our rear wheels. You'd be surprised at the lack of them. In over 12 years of racing, I've never seen a problem. Money is hard to come by these days. If you just want to tool around fixed on a conversion, save some green, reuse the hub and buy your Mom/Dad/Dog/Cat/Iguana/Girlfriend/Boyfriend/Spiritual Advisor/Grandma*** a nice Holiday gift.
Just a note: I am not recommending to not use a lock ring. I use lock rings whenever possible. His question was CAN it be done. And yes, in certain situations not only can it be done, it can be done safely.
*hub and cog
**with proper pipe strength of course
***grandpa's have a tendency to hoard, so pass that one up