Studio flash makers sell both bare flash tubes and flash tubes with a UV coating to block the UV emissions. Quite a few studio monolights come up on eBay without the UV coating, and I'm wondering if that's OK since I plan to always shoot through a soft box.
In general no, but it depends on the diffuser material used. Many come with UV blocking material, while others do not. The amount of UV produced by flashtubes varies, but it's small. Typically the result of the UV is a change to the color temperature of the softbox, potentially throwing off your shots.