Moe
That's not what I do Nate.
When I leave the office the projection is set in the data collector, in this case I have already established control points. The base point I'm wanting to use isn't safe that day, the ranch turned out three horses and they won't leave me alone even to set up, or there are a herd of hungry cows.
I just set the antenna on the mag mount on top of the truck, start it as a base point and locate my control point say 50' away. I then recalculate the new base point on the truck, relocate the control point (usually it's .01' or .02' "off") and I'm off on my 4 wheeler to locate section corners or whatever I'm doing that day. Usually I'm checking existing points all day long, which checks my truck point.
Don't get hung up on localization, I've never done that in 20 years of RTK. Once in a great while I will calibrate, but it's so rare I can't remember the last time I needed to do that.
There isn't any rotation, it's all done inside the same projection, state coordinates, utm, ldp, doesn't matter.
Moe
Nate, you could tie to all four points that are only fifty feet apart from a base a mile away and use all four in the localization, provided the software allows you to disable the rotation, then each of the four points would contribute to the translation, but rotation would be defined by differential GPS (RTK) and the projection (as Moe said, doesn't matter - SPC, UTM, LDP, etc.)