Call the inpatient treatment center and ask if you have a choice about the suboxone or not before you are admitted. Also ask how long suboxone treatment is planned; sometimes this may be as short as a few weeks or more than a year.
If you don't want to use the suboxone method and that is your only alternative with this facility, you might want to consider finding a different treatment center that offers you other choices. I think that it is important for you to be an active participant in your treatment plan, with all options explained to you, including the pros and cons and why one plan might be preferred over others.
One other piece of advice...if you are taking other medications, discuss this with the facility before you are admitted and ask if you will be allowed to continue to take those meds. I was taking Klonopin as prescribed for vertigo and this was abruptly discontinued by a treatment center. The withdrawal was horrendous and no one had explained what it would be like; I ended up discharging myself AMA (against medical advice).
As far as your medical record is concerned, HIPAA protects this information. The only was that your employer should legitimately find out about this is if you disclose it to someone else.