The advantage is that you save resources by tapping into e.g. Connections by taking advantage of the search service it already provides. No need for extra crawlers and indexing efforts.
However: it can happen, that the relevance score provided by Portal versus Connections versus Quickr do not compare, e.g. one of the three tends to score higher than the other. E.g. it could happen that Connections results will tendency wise rank in average higher than those of Quickr.
If this is important, the only chance is to maintain all information in a single search index, and thus have them correctly ranked by that one search service. So we're back spending the additional index and crawl overhead.
However: it can happen, that the relevance score provided by Portal versus Connections versus Quickr do not compare, e.g. one of the three tends to score higher than the other. E.g. it could happen that Connections results will tendency wise rank in average higher than those of Quickr.
If this is important, the only chance is to maintain all information in a single search index, and thus have them correctly ranked by that one search service. So we're back spending the additional index and crawl overhead.