There is some excellent information out there about feeding live. None of that information includes leaving a live, grown mouse unattended with a snake overnight.
You can feed your snake live, you just have to do it responsibly. Most owners that i know feed live give a snake 20 minutes or so (where they keep an EYE on them) to eat. If they do not eat in that time the feeder rodent is removed and kept until the next feeding attempt (5-7 days later). I always recommend pre-scenting before feeding. Leave the rodent out in a container that will allow your snake to smell it for 30-60 minutes before feeding. This should get your snake into feeding mode.
Some snakes switch to F/T easily without a hitch, some dont. You may need to work with your snake to get it to take F/T. This may include weeks of not feeding (because of refusals) or doing a zombie dance, etc.