I know I'm 5 years too late here, but as a network engineer the information here is not accurate and I've already posted to the reddit post about this; also 5 years too late.
First, a VPN adds security as stated above.
However; it does accomplish something of significance, especially for streaming. With a VPN you are staying ahead of standard issues like packets being out of order, missing packet information, and various other issues that can occur in communication.
To put it in layman's' terms; the VPN repairs issues inside of the tunnel, before the end-user sees them. Reordering data, and re-requesting missing data before it is displayed. A website like Twitch can only do that after the issue is seen by your viewers, since it attempts these things.
To answer the initial question: yes, you can have OBS go directly to the internet, while the rest of your computer utilizes the VPN. This is done in two-parts. Creating a route in your routing table that provides a path from the network adapter to the internet, and Using windows defenders' advanced features, which are "application-aware" to create a rule to send traffic from OBS to the route you had created.
There is no easy way to do this, and you'll have to do some learning to accomplish this. Networking is a college degree for a reason after-all, but researching those two things should get you there.