Sure.
The flow rate through the 1" drains (and thus through the sump) will be a function of the size of the return pumps you use to push water back to the display tanks.
It's a closed loop system ... the drain from your tank's overflow (to the sump) will not be greater than the flow rate of the return pump (back to the tank).
The challenge supporting two tanks from one sump comes down
(1) to watching the relative elevation of each tank ... as long as the sump is always lower that the overflow of any given tank feeding it, you will be OK.
(2) making sure the sump has enough free volume (i.e. max volume minus the running volume) to accommodate back-draining of the return lines to the sump in the event of power loss. And here you can cheat a little by using high-quality piston-check valves installed in the return plumbing as close to the tank as possible (NOTE - I'd advise staying away from swing-check or tilting disk-check valves as they will slowly leak and drain your whole return line if given a long enough power outage)
Otherwise, I think you are absolutely on the right track - 1 Apex system supporting one sump. If you want to be really smart, use Neptune's COR-20 or COR-15 return pumps along with an FMM a two 1" flow meters - then in your Apex you can actually track flow rates and the health of your pumps to minimize surprises.
