Do sun-synchronous orbit pass any spot around Earth at a specified local time? If yes or no, what is the reason? (I know that this type of orbit passes everywhere at the equator at the same local time.) thank you so much.
Sun-synchronous orbits take advantage of the precession of the ascending node due to orbit perturbations (primarily the $J_2$ spherical harmonic due to the slight bulge in Earth's shape at the equator). By choosing the right combination of orbit altitude and inclination, that precession can be set to take 1 year so that the local time remains the same at each location in the orbit. The required inclination is typically quite high, resulting in a polar orbit.
That orbit is not synchronized with the Earth's rotation, so the satellite does not pass over the same longitude each time it crosses the equator. See the last figure on this NASA page:
Remember that local time is... well... local! There is continuously a spot (an entire arc, in fact) sweeping across the Earth where it is noon -- the best time to take photographs with the Sun at your back, which is usually why you use a sun-synchronous orbit in the first place.
So, are sun-synchronous orbits possible for any place on Earth? Well, there is nothing really special about sun-synchronous orbits when it comes to coverage in terms of location (just the timing). For an orbit to pass over a particular location on Earth, you just need to have the right orbit inclination for that location's latitude (Deer Hunter hinted at this). How often you pass over the location depends on the orbit period, and it is possible to have orbits that are in some resonance with Earth's rotation (hence they only pass over particular regions repeatedly... like geo-synchronous orbits) -- but let's ignore that since most orbits will eventually cover all longitudes. Sun-synchronous orbits are high-inclination, and the tilt of the Earth's rotation axis means that the orbit will eventually cover all latitudes as well. So sun-synchronous orbits can cover any point on Earth.
In short, yes, sun-synchronous orbits are possible for any location on Earth.
Do sun-synchronous orbit pass any spot around Earth... (emphasis added)
Sun-synchronous orbits use the strong $J_2$ component of the Earth's gravity to precess their ascending node all the way around the Earth's axis once per year.
Since the Earth's axis is tipped by ~23 degrees with respect to the ecliptic, it is important to remember that this precession happens relative to the Earth's axis and equatorial bulge, and although it happens to be synchronized to the Earth's orbit around the Sun in a 1:1 ratio, it does not have anything specifically to do with the Sun.
Rather, the orbital plane slowly rotates around the Earth's North-South axis once per 365+ days. Think of a piece of paper pierced by a pencil, and then tilted. Now think of spinning this around the pencil once a year without changing the way the paper is tilted on the pencil. It does not matter that the pencil is tilted 23 degrees relative to some light bulb 150,000,000 km away.
The equatorial bulge, and all other gravitational effects have only a very tiny effect on the orbit's inclination over time, so for practical purposes you think of the inclination as nearly constant, at least for decades.
That means if the inclination of the orbit were say 60 degrees, it would never pass over latitudes higher than 60 degrees. Even if it were nearly polar at say 98 degrees, it would never pass latitudes higher than 180-98 = 82 degrees.
So no, not any point.
...pass (a) spot around Earth at a specified local time? (emphasis added)
I'm guessing you mean it would regularly pass over (a) spot at the same time each day. That would be a special case of the Sun Synchronous orbit with an approximately repeating ground track as discussed in this Technical details section. For example, if the altitude of a circular orbit were 901 km and the inclination were about 99 degrees, it would orbit 14 times per day and for a spot that it did pass over, it would do it at roughly the same time each day.
See the answers to Are there terms for Earth orbits with rational number multiples of 1 sidereal day? for more thoughts on this.