No... but yes.
Let me explain...
If you take that major scale, the 5th degree's chord will always be a major triad.
However, the minor scale is more complicated. Since there's 3 of them (harmonic, melodic and natural) you can use all of them to create triads. And even though when it comes to chords, the harmonic minor is the one which is the most used (the name gives you some hint there).
So in a natural minor scale, you'll get a minor 5th degree triad, while in both others you'll get a major one. This means you can actually choose whichever you prefer as your dominant.
Then you get to secondary dominants. To simplify things, let's take your example, in D minor.
So if you chose as your dominant a major chord (A7) then you get back to dominants of major chords which are always major. So you'll get as secondary dominant E7.
Now, if you chose Amin as your primary dominant then you could also choose as secondary dominant a minor chord. You could have Emin as secondary dominant.
And this keeps going. It means you could have something like this:
C#7 --------- F#min --------- Bmin --------- Emin --------- Amin --------- Dmin
V7/Vmin -- Vmin/Vmin -- Vmin/Vmin -- Vmin/Vmin ---- Vmin ----------- I
Okay, this would probably sound like shit but it would syntaxically by perfect.
Another interesting thing is about 9ths because in a minor scale, the 5th degree could be either 9 (melodic minor) or b9 (harmonic minor). While in Major, you'll never get a 5th degree with a b9.
So to summarize:
In D Major, your dominant will always be A, A7, or A9, and thus your secondary dominant will always be E, E7 or E9.
In D minor, your dominant could be A, A7, A9, but also A7(b9) and Amin. Your secondary dominant could be:
- If your dominant was major: E, E7 or E9;
- If it was minor: E, E7, E9, E7(b9) or Emin.
And of course, that's if you omit 11th and 13th, 6th and suspended chords, and much more.
P.S. It's fun to realise that your forth degree in melodic minor (ascending. Oh... I forgot about ascending and descending melodic minor! Even more fun!) is actually a dominant 7 chord. It's however rarely used. I've only seen it once in Gluck's Orfeo, act II, number 18, maestoso, measure 4.