No - your back hub is threaded for a freewheel, not a cog.
You have a few more choices to make it fixed, from most recommended to least.
1. Get a new back wheel. Cheapest, easiest method, wheels range from 60 dollars and up for a decent formula to alexrim.
2. Relace a new hub to your old rim. Not advised, the rim on the se draft is decent but is not going to be worth the labor for the lacing up @ the LBS. If you can't distinguish a fixed hub from SS than you probably shouldn't lace your own wheel.
3. Suicide hub. Loctite a cog onto the freewheel threads. Not advised. See option one.
Or ride it singlespeed. Theres nothing wrong with that.
& don't let anyone on the forum tell you the SE is a piece of crap that should be left in the dump. It is good for the occasional rider that doesn't ride on the track but needs a working, easy to maintain bike to get around town with. I liked mine, honestly.