How does administrating and bureaucracy affect being Unit CO and is it worth putting points into either of them?
They don't affect the Dragoons Rating.
They are required for some mission types. Bureacracy in particular gets used for this in defensive contracts.
They also form a soft cap on the size of the overall unit, and administration in particular limits the total number of admins the unit can hire. We just haven't run into that yet because Jon has a good score. The higher of Bureaucracy or Administration, times 3, plus three, is the total number of lances the unit can have. So right now the overall unit cap is 12 lances but again, we haven't run into that so it hasn't mattered.
Finally, random events can pop up which require skill rolls on behalf of the Unit CO or the Lance COs. We just left the initial 2-year "probationary" rules period, so I'm expecting that to start popping up relatively soon. The skills which get called for are actually what determined which non-combat skills I retained from MechWarrior 3e. Basically, there are no safe "dump" skills.
That said, Rob also has a tendency to ensure skills are used to people’s benefit or detriment depending on how specialized characters get.
On top of all of the above, there is also this point. Again, I don't believe in dump skills or stats. Everything can be important, and while certainly piloting and gunnery are the skills we end up using most because we're playing BattleTech, ALL skills can and will come into play, or they wouldn't exist. The most important skill in the game is whichever one I'm telling you to roll right now.