Questions about NYC insurance coverage of penile implant surgery

I currently have HealthFirst medicaid and live in NYC. I started working last week and am offered Oxford insurance thorough my employer. I'm scheduled for penile implant surgery in December through HealthFirst. I'm single, not married. I have some questions:

1. Should I ask my job if penile implant surgery is covered through their insurance? If I ask them would I get fired since its an expensive surgery?

2. Since I started working last week, will HealthFirst find out I started working and will they deny my surgery?

3. Has anyone here had Oxford insurance pay for their penile implant surgery in NYC?