Yes, if I can recognize triads, 7ths, and 6ths in their different inversions and know which note is the tonic then that would get me most of the way there. Minors and Majors would be a bit harder to see, that would require more familiarity with the different keys, no?
Not really. Standard notation is oriented around the diatonic scale pattern, and if you know which degree of the scale serves as the root of the chord (which, if nothing else, you can figure out by counting lines and spaces from a tonic of the key), you know what type of natural chord to expect: in a major key, the natural I, IV and V triads are major, II, III and VI are minor, and the VII triad is diminished (functioning as a rootless V7). Accidentals will show you when the chord is altered from typical expectations
and in which direction, and they seldom appear in chords natural to the key except when restoring a pitch altered previously in the measure. Consequently, standard notation makes it far easier to decipher and name chords than tablature does.
In major and minor triads, you have only third and fifth intervals (inverted, these are sixth and fourth intervals, respectively), making it easy to spot the root: look for the fifth (bottom note is the root) or fourth (top note is the root). If you have two notes a 7th or 2nd apart (the inversion of the 7th), you probably have a 7th chord (root at the bottom or top, respectively). Alternatively, you might have a 6th chord (2nd/7th interval between the 5th and 6th components of the chord). 2nds really stand out, because one of the noteheads has to be moved to the opposite side of the stem. The key to spotting 7ths is that they both lie on a line or both lie on a space, with two other lines/spaces in between. If you have no 3rds or 6ths, it's probably a sus4 or sus2 chord. Few chords fall outside of these common, easily identified patterns.
Admittedly 9ths, 13ths and 6/9 chords do, and can be tricky to decipher, particularly when rootless, and sometimes the same set of notes can be interpreted in multiple ways, so you have to look at progressions (or fuller arrangements) to figure out what the root is and what type of chord is built upon it. For instance, some 7th, 6th and rootless 9th chords all share the same set of written pitches (and uke chord shapes), but make differing harmonic "sense" in a given context.