Donations are subtracted from the taxable estate when the estate tax is called into effect. This provides an incentive to donate rather than incur the hefty estate tax, which takes (in 2014) 40% of the estate value over around $5 million. In fact, the Congressional Budget Office published a report on the subject, found here: http://www.cbo.gov/sites/default/files/cbofiles/ftpdocs/56xx/doc5650/07-15-charitablegiving.pdf, wherein they estimate that, with the repeal of the estate tax, 6-12% of charitable donations would disappear.
No, eliminating the estate tax would not reduce charitable giving because there would be more money for people to work charities into their estate plan. Many people feel that because the government taxes their estate, there is no need to also give money to a charity when they die. Freeing this money up would make people feel responsible to charities as well as their children.
I don't think the estate tax would reduce charitable giving. It may make it harder to give property, but for the most part, loved ones receive inheritances and property at the death of a family member. I doubt this tax has a lot to do with charity, if we eliminated the tax, families may be upset that it's not as easy to resume ownership of those possessions. Charity may be affected, but I think individual families will be affected more.