It'll run.... but with no downpipe you'll spew hot exhaust gas right at your firewall and everything on it, probably melting everything. You won't see a powergain since it isn't connected to any intercooler/intake piping, and ironically that would be a good thing since if you did boost, with no wastegate you'd run some insane amount of boost and you'd blow up the engine. At least, untill your turbo blows up from not having any oil in it.
Here's a link to everything you'll ever need to know about turbos
And if you can't find what you need there, it'll surely be here