Can I get a DC output if I connect my laptop AC adaptor to a battery?
Your proposed  connection of a battery to the   AC input of the Laptop PSU will not be good  .The  DC needed to make sure that the PSU produces enough output and does not overheat could be say 100VDC which means that you should not play around with it if you do not know what you are doing .The internal fuse in your laptop PSU will be specified for AC .This could mean that under fault conditions the PSU could burn your house down if not backed up by a proper larger more expensive DC rated fuse .Laptop PSUs designed to run on AC are optimised for cost and not efficiency .This low efficiency will make battery operation not optimum .