Since the modes are derivatives of standard scales ( or possibly the other way round), then yes. Take the chords produced from C major. C, Dm, Em, F, G, Am, Bo. All based on 'stacked thirds' - not exactly true, but for our purposes...Of course, another 'stacked third can be, and is often put on top, and maybe this is where your dilemma starts, as each third can be maj or min, BUT without care, the chord notes go out of diatonia.
The same notes appear, in the same order, in D Dorian, E Phrigian, F Lydian, G Mixolydian, et al. So, keeping the 'stacked thirds' idea, in D Dorian, the same chords appear. They have to. It's just that now, as in any Dorian melody, the home is based on the root, in this case, D. So the home chord has to be Dm. In G Mixolydian, obviously G maj appears, and quite often in G Mix. tunes, F maj also appears.
The minors present a slightly different arrangement, with the possibility of raised 6th and 7th notes, or not as the minor case may be. However, all chords used in minor modes will be made in the same way - 'stacked thirds'. So there are more options of slightly different chords in the modes of minor keys. Simple example, in A Aeolian, there are two E chord - E min and E maj.