You can take secondary characters. Your roster is selected from your race's list as per normal with the exception of the FC. You select your fleet from your roster.
As to whether or not I'd allow people to do so, yes, I don't see why not. Characters aren't terribly impressive most of the time.
Regarding the apparent incongruity of secondary commanders having higher Ld than their FC, I don't really see a problem with this. There could be a good number of reasons for this. Politics can see a less competent or skilled person assume command. This could be due to personal charisma, nepotism, inheritance, machinations, or as a matter of policy (fast tracking certain promising officers over more experienced personnel). The FC could even have been the best candidate at the time, and promoted to lead a large force, while the secondary character might have joined later with a much smaller force. Also, the extra burden of coordinating an entire fleet, as opposed to a ship or squadron, may lead to a dip in apparent efficacy. So any Ld 8 secondary character given the task might also drop down to Ld 7. Lots of possible scenarios. All this doesn't even take into account the fact that Ld doesn't really represent tactical capability, not in-game anyway. It's more a reflection of crew competence.