Rand Paul is fully capable of running for two federal offices in 2016. This is largely because he faces absolutely no tangible threat of being removed from his seat as a senator representing Kentucky. The state he represents is almost certainly going to re-elect whatever Republicans are on the ticket so his inevitable failure of a Presidential campaign should have no impact on his run for re-election as there is very small chance he will ever get the Republican Presidential nomination.
No Rand Paul will not be capable of running two federal offices in 2016 he should pick one and let someone else do the other. There is too much of a chance that something could fall through the cracks better to divide the work then try to take everything on.
Rand Paul can not effectively run two campaigns at once. This shows that he truly is not committed to either one. He will lose votes based on that idea. Running for two offices also creates a conflict of interest. What if he wins both? Does he choose one, or will he serve in both? It is just simpler to pick one to focus on and concentrate funding there.
The problem with Rand Paul is that he's all talk, less a policy maker than the sort of guy who does a filibuster for brownie points and makes the media rounds congratulating himself. That's what he's good at, congratulating himself and telling everyone to love him. Running two offices at once, how's he going to have time to orchestrate a media circus?