Ah, well men obviously have more upper body strength than women, so that might make it more viable for you. I still say the treadmill would be better overall, but if you can make the arm thing work, then go ahead and work it!
Also, and excuse the preaching, the exercise can't stop just because you reach your goal! It's important for your overall health as well as weight loss maintenance.
Take the free arm bike and use it for a few months. You can re-evaluate your fitness needs further down the line.