As long as the SIP phone conforms to the respective SIP RFCs, yes. You'll have a more limited feature set than a Cisco phone which uses proprietary SIP extensions to add more functionality than the SIP RFCs provide.
The 3rd-party SIP phones will consume a lot of DLUs (five or six I believe) so make sure to account for this.
On a side note: I would be very apprehensive as the partner if the customer is trying to put multiple wireless phones in without a reliable, controller-based (from Cisco or elsewhere) wireless infrastructure that has been designed to support voice.