In real-time precise point positioning (RT-PPP), PPP one-way timing is used to steer local oscillators, but the timing performance could be significantly affected by the datum stability of the satellite clock product. To measure the stability of a satellite clock datum relative to the hydrogen maser (H-MASER) clock, a new GNSS satellite clock datum stability assessing model based on the overlapping Allan variance (AVAR) is proposed for both PPP one-way timing and time synchronization. Experiments were carried out with nine Global Navigation Satellite System (GNSS) stations at time laboratories with an external H-MASER clock to analyze the datum stability performance. In the experiments, RT satellite products from five RT Analysis Centers (ACs): CNES, ESA, GFZ, GMV, WHU, and the final satellite product from IGS were used in the comparison. Results show that the datum stability of all RT products tended to be similar, i.e., 6 to 8E−15/day, where WHU and GMV outperformed other RT ACs. Moreover, these datum stability results indicate that RT-PPP for steering local oscillators improves stability to 6 to 8E−15/day when selected with an appropriate RT product. The estimation noise in all RT ACs was at about the same level, i.e., 1 to 2E−15/day, but WHU delivered the most stable performance. Thus, datum stability is an effective guide for setting parameters and making long-term stability predictions when steering local oscillators, and satellite clock datum stability can be measured conveniently and quickly using the GNSS satellite clock datum stability assessing model proposed in this paper.