yes it is possible, yes it should be fine.
Below is some maths (that I hope helps) -
1 mol of glucose weighs ~180g. You have 1.3 us gal ~ 5 litre (4.9....) of fermentable liquid, I will say 5 is much easier to work with here.
At gravity of 1070 you have roughly 1 mol/litre. (182.5g/l)
If we assume that during feremtation roughtly 1 mol of glucose yields 2 mol of CO2.
Then 5 litres @1070 fermenting down to roughly 1000 will yield 10 mol of CO2. And given that 1 mol of CO2 at room temp and 1 atmosphere of pressure fills ~24 litre or 6.3 USGal, our 10 mols of CO2 will fill 240l, or 63 US Gal.
I would say that any worry about headspace O2 vs CO2 is unfounded.
NB - if you did this in a pressure vessel of 30l... with 5 litres of uncompressable fuild(your fermenting must/wort), and never allowed any CO2 to escape ... the pressure would build and you would be (assuming the yeast ran to completion and diastatic pressure did not kill the yeast) end up with 240l in 25l headspace, or a very dangerous pressure vessel, unless you had a pressure regulator/saftey valve on there.