An interop calls something else, it's an interoperability assembly, so you're inter-operating with something...in this case Excel, the actual installed Excel.
In this case yes, it will fail to run because it depends on excel, you're just calling excel functions. If they don't have it installed...out of luck.
There are methods to generate without Excel, provided the 2007 file format is ok, here's a few:
as I said though, this is the 2007 format, normally if anything, that's the deal-breaker.