If there is a droop in the chain you may never get it tight enough to take it all out, and it will be putting a lot of stress on your sprocket shafts. You may be able to add enough idler sprockets (top and bottom chain sections) to keep the chain well supported so that there is not so much tension required, but, if the chain links run bottomed out in the sprocket grooves, it will never be very close to a "zero back-lash" system.
Getting the perfect long chain setup is why I think it has generally been discouraged around here in applications where precision is required. Short chain lengths fair better but there are better ways to do this. Usually in the form of ACME rods or ball screws.