Will I see a productivity increase if I use Qubes OS?

Let's start with a ground truth — the main motive people have to install Qubes OS is rarely productivity.  You'll probably experience decreased productivity due to the fact that you must deal with multiple compartments.  The main motive is usually a desire for a heightened stance in computer security, and this itself is rarely conducive to more productivity.

However, for certain use cases, you will definitely see an increase in personal productivity.

For example, if you are a software developer, who develops and tests software in different environments, Qubes OS is extremely useful.

• The ability to stand up an ephemeral environment quickly, have multiple environments completely isolated from each other, and to test complex multi-application setups are indeed Qubes OS strengths.
• In addition to total isolation between environments, its software-defined networking (exploited by add-ons like Qubes network server) excels at letting you do these sorts of things.
• You can also develop and test for multiple OSes on the same machine (various flavors of Linux, Android-x86 via Anbox, and even Microsoft Windows) — with ae user experience substantially better than the trouble of having to deal with multiple physical boxes.
• Since everything is local, your development will go much faster than, say, having to do the same things over latency-high SSH connections to multiple cloud machines — and, of course, GUI applications integrated in Qubes OS just work better than, say, over VNC or RDP.

So, given the right use case — and adequate hardware for it — yes, it's possible that Qubes OS will increase your productivity.