My understanding of FBA is that each SKU can have multiple suppliers, and stock is assigned to its supplier as it arrives in the warehouse (e.g. 250 Anker chargers with SKU ABC123 from AnkerDirect arrived May 22nd and are stored in warehouse X, unit Y, location Z). An order for a SKU from a specific supplier (e.g. ABC123 charger from AnkerDirect) will be taken from that stock, and the quantity remaining is reduced accordingly.
So, to answer your question: if that all happens, and assuming AnkerDirect doesn't have shady stock, then yes, it should be genuine.
It depends even more on whether there are any sources other than Anker Direct for those branded products. If they're the only source and Amazon is their only channel, then any other seller is either counterfeit or purchased through Amazon and is now trying to resell.