Hi there. Just leaving the water is likely safest for your liner if you find your test shows the water you added is normal in terms of TA and ph. Algae, for sample, can't typically grow in water that's under 60 degrees, so if you hook up your equipment early enough in spring you might avoid the swamp effect.
Your issue with Pool Antifreeze (under NO circumstance use auto antifreeze) is that you do not have your equipment set up to get it back out of the lines and while its not harmful to the same scale as auto antifreeze (which is downright toxic) you don't really want to blow it back into the water on set up (may fight chlorine, increase ccs, smells odd, etc.)
Usually in spring, the guys here start up by pumping to waste to get rid of the antifreeze. Not sure what installation of equipment requires in terms of getting the water flowing and priming the pump in your case, so perhaps there's no reason you couldn't do exactly the same...are you self-installing or having the work done for you? If you're having the work done, you might ask installers their opinion.
Re: cover...I'm assuming you're aware that's not a safety cover (which typically cost a few thousand but last years and semi-permanently anchor to the pad via springs and bolts...the difference is high grade strapping that will handle high loads) and that your pool is otherwise secured from any humans/animals via fencing etc. so the cover is more to avoid leaves etc. from getting into the water.
When house hunting a few years back I saw folks use those types of covers with water bags so they must hold up to the snow okay...my pool's really close to my house and en route to a poolhouse/guest house type of structure which is likely why mine came with the pricier but more robust winter cover.
Good thing too as my son's visiting Siamese kitten, known as "grand-kitty" promptly walked across it the week after I closed the pool. He was quite mystified as to where the sparkly wet stuff had gone
