No, because you are passing only a relative tolerance rtol. That means it will still probably fail if t[1] - s[1] happens to be nearly zero.
Yes, using atol is safer, but requires you to pick a reasonable atol, and that depends on the problem because atol is dimensionful.
For example, suppose your vectors represent positions of stars in the galaxy, with coordinates measured in meters. Then atol = 1e-3 (1mm) is probably a ridiculously small tolerance. On the other hand, if you are doing atomic physics with distances in meters, where the typical scale is angstroms, then atol = 1e-3 is a ridiculously large tolerance.
This is still likely to fail if any element of t happens to be zero or nearly zero.
Note, by the way, that ≈ works perfectly well on arrays, or arrays of arrays (anything with a norm), so using ≈ with all is generally unnecessary (and more susceptible to scaling problems). You can just do s .+ Ref(mean(t-s)) ≈ t (no dot on the ≈), which is more robust although it will still be problematic if norm(t) == 0 (maybe that is less likely … but ultimately you should still be thinking about an appropriate problem-dependent atol).