Hi Christian,
the search in WebUI goes on table CRMD_ORDER_INDEX. It is an index table where for each maintained partner in the ticket an entry is created with ticket guid, partner function and partner id.
The problem with your request is, that there is no index entry for an empty partner function, so the search is not able to find such an entry.
The only solution is to select the tickets with the standrad search parameters and than loop over all result tickets, get their partners and check if your partner function is empty.
The big problem here is that the performance is awfull if you have many tickets in your system.
SAP does this in the home screen widget "My Messages - For Dispatching":
See CL_AIC_IM_M_BSPWDCOMPONEN_IMPL->GET_QUERY_RESULT , line 360
Hope this helps,
Christoph