Most softboxes actually attach to the strobe the same way the reflectors attach to the strobe. So it's one or the other and not both at the same time. I'm wondering now if we're talking about the same thing here with "reflectors." My strobes are bare bulb inside my softboxes. The exception is my Lastolite HiLite, where I do use reflectors on the strobes, and my Lastolite kicker light box. Many softboxes provide multiple layers of diffusion material you can use to change the characteristics of the light. You want a wide spread of light inside the softbox to use as much of the surface area as possible to your advantage. A reflector would defeat the purpose.
Bare bulb strobes for background lighting are probably going to cause a lot of light to spill onto your subject and maybe even cause lens flare. Some sort of modifier is typically used to control the light and make it go where you want on the background. You can use reflectors with or without grids or whatever you like. I often use strip boxes for background lighting when not using my HiLite...and maybe a strobe with gridded reflector for a spot of light directly behind the subject. Just depends on the look you want.
Cameras: 1DX, 1D4, 20D, 10D, S90, G2
Lenses: Canon 10-22mm, 16-35mm f2.8L II, 24-70mm f2.8L, 70-200mm f2.8L IS, 300mm f2.8L IS, 200mm f2L IS, 50mm f1.4, 50mm f1.2L, 85mm f1.2L, 1.4x TC, 2x TC, 500D macro, Zeiss 21mm
Lighting: 580EX, Elinchrom 600 RX's, D-Lite 4's, ABR800, 74" Eli Octa, 100cm/70cm DOs, Photoflex Medium Octa and reflectors, PW's, Lastolite Hilite, Newton Di400CR bracket