Congrats on your new (to you) RCA CTC7 "Whitmore" color TV.
I'll be looking forward to seeing pictures of it in operation once it's restored. I am always interested in this type of restoration, where an old TV or radio is brought back to life after years or decades of storage or disuse. Once this set is restored and working again, it will work perfectly well with a DTV converter box and an antenna; just be sure the set's VHF tuner is set to channel 3 or 4 to receive the output signal. Since there is no more analog VHF or UHF TV in the U. S. since the DTV transition, it shouldn't matter which channel is used.
BTW, that "mystery accessory" you show in your post is actually a remote control unit for a Philco console radio; I don't recall what year. The controller must have come from Portland, Oregon since the tuning presets are all (or mostly) Portland radio stations. (I live near Cleveland, Ohio, but I do some AM radio DXing from time to time using a Zenith C-845 and am an amateur radio operator, which is how I know about Portland's radio stations.) If you can find the radio this controller goes with, you will have an excellent beginning to an antique electronics collection, if you don't have one already.
Good luck.