Too Much?

Will large amounts of running and swimming inhibit my ability to gain strength (endurance strength) in my PT, including pull-ups, push-ups, and dips? My volume isn’t up that high yet, so I haven’t noticed a problem, but it’s going to get more intense as the weeks go by.

If you are raising your volume of GPP or whatever you want to call it you should lower the volume of your lifting. There is an excellent article titled Push/Pull at elitefts.