the BES Client Setting: Client UI Minimum Analysis Interval task in the BES Support Site. The forum post MinimumAnalysisInterval with v9 clients using offers and the forum post Besclient using high cpu.
None of these references mention this client setting having an effect on the speed at which Analysis Properties are reported at all, and only mention their effect on CPU usage of the client, as well as their effect on the Client UI.
The BES Client's Minimum Analysis Interval setting controls how frequently the BES Client evaluates action progress information and updates the BES Client UI with new information. Raising the Minimum Analysis Interval will cause the BES Client UI progress information to update slower but will allow the BES Client to report information on Fixlets, Properties and Actions to the BES Console faster.
This leads me to believe that this setting could be increased to 15min with no ill effects, unless there are offers, or other info being used in the Client UI that depend on this value, in which case it should be lower. I think this is likely due to the Client UI using Session Relevance, which would be one of the few things effected by the analysis results reporting interval.