TF-160 of the '03 manual shows the oil pump on the back of the transfer, accessible by removing the tailshaft housing, geared off the rear output shaft (actually looks like it's running off the speedometer drive gear). Based on that, looks like it should pump regardless of what the front end is doing. And yeah, I'd expect it to behave about the same as unlocked hubs. You might get a light on the dash if the control unit for the transfer gets confused--IIRC some of them determine front wheel speed from the ABS sensors, and some watch a sensor on the front output of the transfer, and the latter system gets understandably confused when it sees what looks like a rolling burnout at highway speed for hours. AFAIK the transfer itself doesn't notice or care.
TL;DR, yeah, should be fine.
If it doesn't vibrate with the driveshaft out, that points to the driveshaft. I haven't messed with the U joints on mine, but I've heard they can be a PITA to get balanced again afterwards. The PD section of the manual shows a bunch of different thicknesses of snap rings that I assume are used to get the end-play correct. Worth a look if you haven't yet.
I remember one case where a guy had a vibration only in 4x which IIRC came down to his front diff bushings being so trashed that the diff was moving and screwing up the U-joint angle when the front end was loaded. Doesn't really match your symptoms, but it's the only other thing I can think of that would cause a front-end vibration that isn't tire wear or bearings or something along those lines. My money's still on the driveshaft.