Modding a single cell power bank
Yes you can put Li-ion cells in parallel, and yes they will charge, though they obviously will take longer to charge. There are many considerations (cell capacity, charge state etc) in putting cells either in series or parallel, but with only two cells I doubt many would be of concern to you. There are many 2-4P batteries in the RC community.

The only warning for you is to either fully charge or majority discharge (I always discharge on my Li-ion charger) your cells before connecting them together. Once connected together give them at least 15 mins to stabilize before attempting to charge them as a single unit.  

You might read through something like this or many other good texts related to care and maintenance of RC battery packs to gain more knowledge.