I have made alot of batches, draining the tun to a bucket with plans on doing the boil in the morning. No problems encountered. In fact, I let the wort settle out overnight and siphon to my brew kettle in the morning. It's amazing how much flour will settle out overnight. I do put the lid on and plug the hole in the lid with an airlock or paper towell.
For lagers, you can make a little extra wort, use that for your starter and let the boiled wort sit in the lager chamber for a few days cooling to 50 while your starter takes off. After cooling the wort, siphon again to ferm bucket and leave trub, hot break and hop debri at bottom, aerate and pitch. This way you get a clean yeast cake for the next batch(only use half).
Same procedure is fine for ales. I have made about thirty batches this year, no infections, no problems.