Run a test roll and see for yourself. Set up a portrait or still life subject with whatever you consider a "normal" amount of ambient light (room lights on? modeling lights on?). Shoot a series of frames on each shutter speed from fastest to slowest. Print a contact sheet, and note when you start to notice the ambient light having an effect, and if it's a portrait subject, when you might notice ghosting from the ambient light.

Depending on how powerful your strobes are and how much ambient light you have, you might not notice any effect from ambient light until you get to about 1/15 sec. or even longer. I've used open flash technique with powerful strobes and dim light, where my human-sync speed (how long it takes to uncover the lens, fire the strobes, and cover the lens by hand) can be around 1/2 to 1 sec.