That's a surprisingly involved question and depends on what kind of oscillator you operate how, and what model you apply to assess the stability.
What you probably want to read up on is "Allan Variance", which describes the distribution of phase error (and a frequency error is a linear-in-time phase error) when observing one clock with another clock. Whether or not you interpret random phase fluctuations as frequency error is up to your oscillator model!
The practical problem here really is finding a clock that's significantly better within a 10 s observational window.
Experience, however, tells us that practical communication systems that would require such a ppb stability for their receivers "waste" a lot of channel capacity for periodic synchronization. That's often more of an result of accomodating changing channels (especially in wireless mobile comms), but if you think about fibreoptics, which do have billions of symbols per second, you'll find that extensive clock recovery is done all the time, taking away bandwidth for actual payload data.
That points out that even for datacenter-grade electronics, you can't just plug in an oscillator and hope it runs stable enough for seconds after you initially estimated frequency. So, I'd argue, that even without looking at Allan Deviation in oscillator datasheet, the answer is "no, PPB stabilities are the domain of atomic clocks, very expensive oven controlled oscillators, or GPS-disciplined oscillators".