Most hospitals (and other employers) do not specifically test for Suboxone, unless there is a reason for them to be concerned. The usual test for opiates will look for morphine and its derivatives, so Suboxone, which is synthetic, is not typically detected by this test.
As I said above, most hospitals do not test for it. It is true that some employers have started testing for it. For example, if in a community in which there is more of a problem with recreational use of Suboxone, employers might decide to test for it. As the other expert noted, if you have a valid prescription, it still would not be held against you. However, if you feel that you would rather avoid that issue, you may need to discuss with your physician if you can perform an accelerated taper.