It is very important to keep track of the click sequence before conversion while using more than one channel for a particular campaign. This is very important to apply correct attribution to each media and also to understand how all the different media channels are helping or cannibalizing each other.
The overlap in Search and Display is very high; I have seen numbers as high as 33%. This number could be even higher for products if there is very long research phase like buying a higher priced item example laptops.
There are some advanced reports in DoubleClick's DART (Exposure to Conversion) report which provides the last 10 clicks (by site, placement, time) which helps understand which publisher engaged the most consumers for the first time and then which publisher led to most conversions with least number of other publishers coming in between the first click and conversion.
Some other cookie based systems can provide overlap across all channels – email, search, display, affiliates (DART cannot provide this as DART tracks only Search and Display).