Can I use this drain in wood subfloor?
Yes you can.  I have done a few drains on second floor laundry areas.  This is perfectly acceptable.

First you don't really pick where the drain goes exactly gravity does.  You need to figure out in what direction water will go in that room from the washer - you need to put it on the low point.  Then you need to chisel out slight the area around it - maybe going out a foot or two and down at least 1/16th of an inch, better if 1/8th.  

Also if you are really worried about what is under the room you might want to redgard the floor or some other sort of waterproofing.