We were running campaigns over many years and recently I did an analysis using the google adwords data on cost per conversion per hour. The costs during the night were very high compared with daytime and therefore I have now stopped adwords showing at all during 10.00pm - 6.30am.
Some businesses, i.e. sleep problem products, will actually have brilliant cost per conversion figures during these hours so make sure you test your data.
No, it can be a bad idea, unless you review visitors and conversions flow carefully.
You should fist check the days and hours when most conversion occurred, check the trends of last two three months. If you find any such day or hour/s when you sell most, then you can accordingly set your bidding.