Will my SB-600 for my Nikon d70s run my off camera Slave flash?

I'm trying to do a little more research before I purchase a SB-600 flash for the hotshoe mount on my Nikon d70s. This camera does not have the slave flash control on it. Will this flash trigger my off camera flash, such as my flash umbrella? I'm looking for a wireless option and I keep reading about this particular flash.

You need to do a LOT more research.

1. The D70 can control the SB-600 itself, without anything in the hot shoe. Unless the flashes in the umbrellas are also Nikon iTTL lights, the SB-600 will have to be set for manual mode to work. If the lights are iTTL, then you already have a controller.
2. You need to read the manual for whatever light you have mounted with the umbrella, although most monolights have an optical slave built in. Now, there's the problem I can guarantee you will have, where the flash on your camera will fire, the umbrella lights will fire, and your pictures will be black. See #1. Optical slaves work, but only if you use them properly.
3. If you want wireless control, you can buy a radio trigger and however many receivers you need off EBay for less than $50. This will be your best bet. Using an SB-600 to set off slave flashes is a waste of money.

Read your manuals for the D70s and the SB600. You will find that the D70s has something Nikon calls commander mode, the built in flash can control the SB-600 when off camera (even if you mount the SB-600 in an umbrella).It's a good system, somewhat limited, but good for some things. It lacks the utility of the Nikon SU-800 commander or a full studio flash system + flash meter but it will expand your photo options a great deal.