Yep. Studio flash will have enough IR in it.
You get problems with odd things like flo. lights and things like that.
In fact a neat trick that many people use is to shoot Kodak HIE with a "black" IR filter on the lens and on the flash. And by this I mean one of those IR filters that ONLY lets in IR light. The ones where you better be using a rangefinder and f/16.
This gives you an "invisible flash". Very cool.
I recal that Weegee used this method to shoot INSIDE movie theaters during the movies!
This can be fun too if you want to shoot someone with their pupils wide open.