Can an astronomical telescope with an equatorial mount be used as a theodolite? (For example, at this time, use declination to adjust left and right, and latitude correction to adjust up and down.

Some equatorial mounts can do this. Most can't. Generally, the polar axis height adjustment range of an equatorial mount is 20-70 degrees. If the right ascension axis can be adjusted to be vertical, it can be used as a theodolite. If you can adjust the right ascension axis to the level, you can use the declination axis to adjust the azimuth and the right ascension axis to adjust the altitude. @First Telescope Store