To fill an SRO instant slot, you'd probably get hired on as "Ops staff" to start -- a management position, non-licensed, which means you would not be qualified to operate anything. Your role, until the license class starts, would be administrative, and you most likely would not get any on-watch operating experience. Very little opportunity to learn the plant, as you'd be involved in administrative work (of which there is plenty of to go around). On your own time, you could always start looking ahead and studying, which might be helpful.
For NLO, the "POSS" (I cannot remember the details of this initial hiring test; just that it was easy) does not require any core theory knowledge... some basic physics, some math.
I also work at a dual unit site... some staffing differences from what Mike noted, but similar... At any one point, seven SRO licensed individuals on watch, assuming the STA is licensed.
Activity on shift is busy. Some time ago (10 to 15 years), commercial plants changed their operating philosophy. It used to be that all potential risk activities (any maintenance work that could remotely jeopardize generation) were saved for refueling outages. Preventative Maintenance programs were bare bones and unstructured. Run till something broke, then fix it; that was the philosophy... not bad for newer plants. But as the plants aged, every week forced outages resulted from equipment failures. Capacity factors (percentage of full power X time) began to suck. Refueling outages became lengthier and lengthier. Maintenance programs were restructured, and the philosophy completely changed. Now, we work anything and everything that can possibly be worked without shutting down the plant. A steam leak? Find some way to isolate it and fix it. A seal leak on a Condensate Pump? Reduce power, shut down the pump, and work it. All work is classified as outage or not, and if it can possibly be done with the unit on line, every effort will be made to do it. The overall result is better running plants with shorter refueling outages. But all this makes for a busy watch team -- on nightshift, you'll find yourself working to shut down and isolate equipment for the following day's maintenance crew. On dayshifts, recovering from the same. Makes it interesting, but challenging.