Yes, you can get the sharped 3rd fret of the treble string (G sharp) by playing it up at 6+ on the middle string.
But, I'm guessing that you want the 3 1/2 fret because you are looking for the "raised 7th" in minor keys. So, for example, you may be looking for a D sharp when you play in e minor. (A lot of folk music uses the d natural in e minor, because many folk tunes use the "natural minor"; but in some tunes and especially classical music the minor scale on which the tune is based is the "harmonic" minor, which has a raised seventh step of the scale (i.e. d sharp if you're in e minor). And that raised seventh may be in the melody line, or we may "hear" it - or what to hear it when we play the V chord (dominant chord) as part of the harmony (so that, would be the b chord if you're in e minor).
I've yet to find a way to get that note (raised seventh) in DAD tuning, not for ANY minor key. (For instance, DAD tuning works nicely for tunes in f "natural" minor, but b harmonic minor needs an A sharp, which is not there). If this is the problem you're grappling with, here are two possible solutions:
1- try tuning in DAC. In that tuning, you'll be in d minor, and you'll have a raised 7th in ONE place, fret 2 of middle string. Sometimes that solves the problem.
2- if the note that you need is not in the melody, but you're wishing for it in the harmony chord---- try staying in DAD. But, when you come to that chord where you want the raised seventh (i.e. in e minor, it would be when you play the V chord, which will come out as a b minor, but if you had a D sharp, it would be a B major chord) try playing a b "neutral" chord, that is a chord that contains ONLY b and F sharp, no D's. You're ear will miss the D sharp, but better than have the d natural which would be even more bothersome, and, in fact your mind's ear may actually let you think that the d sharp is sounding.
If anyone with more music theory background can give a better explanation OR can solve the problem better than all this, please do write in. I have often wished for the ability to play minor tunes that use the harmonic minor, but have concluded (perhaps erroneously) that it's not doable in DAD, and not terribly doable in any tuning, other than chromatic ones.