Gabe,
A good rule of thumb is that for athletes like yourself you can improve one capacity at a time. You can improve your running and maintain your climbing…or vice-versa…but it is unrealistic to try to improve two such polarized physical capacities at the same time.
The exception would be if you’re just starting out and the improvement curve is super steep, say you just started climbing and you can go from 5.6 to 5.10 in a year.
That said, I highly encourage everyone to spend time fingerboarding. It won’t impact your running but it will have huge long term benefits to your climbing. If approached gradually and consistently you’ll have strong and (knock on wood) pretty injury-proof fingers. A great foundation for improvement!