Can this adapter also be used as a charger using the Nomadic Portable Power Block?

The short answer is "probably, yes." Any power source that can charge the iPhone directly using the phone's Lightning-to-USB cable will work just as well plugged into the Lightning jack of your Headphone Jack Adapter. The only caveat to this comment is that some aftermarket headphone jack adapters save manufacturing money by putting a micro USB jack on the back of the adapter instead of a Lightning jack. In that case, you will need to supply micro USB power to the adapter.

not familiar with the product in question

but trying to charge using the 3.5mm connector would not be advisable even if it's a lightning to 3.5mm adaptor