I know the April board has a jumper for USB or batteries on VIN and GND. It also has + and - pads for connecting batteries.
My question is can I connect to the USB female plug on the April with a mini cable and have the other end of the cable connected to four AA batteries rather than a 5V charger ? I assume the jumper would still stay on USB.
Yes that will work. The schematic https://electricimp.com/docs/attachments/hardware/reference/april/april-schematic.pdf shows that both power inputs are tied to the bucking converter input.
FYI: The battery pads have reverse polarity protection connections (Q1), so they are attractive if you aren’t going to be the one changing batteries!