I don't think this should be added. Synapse is meant to be the center of attention while being used, so it can be utilized quickly to accomplish the task you had in mind. Having a search box in the indicator would totally take away from that - there'd be two places to access the same thing, your attention would be split from using the indicator's search box or the regular way of launching Synapse.
Also, the day of the applets are dying. Ubuntu 11.04, Gnome 3, and even eOS are starting to make the top panel a place reserved for a few important system functions, such as networks, volume, time, and a social panel. It's so much simpler like this; you don't have to worry about the panel getting crowded with ugly and unused indicators. Putting a search box in the indicator would take away from this whole movement of clearing out the panel and reserving it for the system/OS.
Just my two cents. :P