This paper presents a feasibility study of using emission tomography (ET) systems for synchrotron X-ray fluorescence computer tomography (XFCT). The proposed detection system combines high-resolution semiconductor detectors with multiple-pinhole apertures. The key advantage of using an ET-based detection system is that 3D distributions of trace elements can be built up with much reduced scanning motion and potentially without need for tomographic reconstruction. In comparison to the conventional line-by-line scanning scheme, the ET-based imaging system allows a great reduction in imaging time, which has been one of the major hurdles for current XFCT studies. In order to compare different imaging schemes for XFCT studies, we developed an analytical performance index that is based on the fundamental tradeoffs between image noise and spatial resolution achievable with given detection configurations. To further demonstrate the feasibility of using SPECT apertures for XFCT, a prototype CCD-based multiple-pinhole imaging system was set up at the Advanced Photon Source (APS) for imaging phantoms that contain solutions of several trace metals. Simultaneously acquired 3D distributions of these elements are presented.